Reactive Power Optimization Method and System for Wind Turbine-Integrated Power Grid Based on Identification of Voltage Weak Points

Abstract

The present invention provides a reactive power optimization method and system for a power grid with wind turbines based on voltage weak point identification. It includes: obtaining the structural parameters and electrical parameters of the power network; calculating the adjustable range of reactive power of the wind turbines connected to the power grid based on the power conversion model of doubly-fed wind turbines; after a large number of wind turbines are connected to the power grid, constructing a node voltage change index, and using the continuation power flow method to obtain the PV curve of each node voltage and calculate the node voltage change index under the critical state to determine the voltage weak nodes in the power grid; finally, constructing a reactive power optimization model with the voltage weak points as reactive power compensation nodes and using an improved weight particle swarm optimization algorithm to solve it. The present invention reduces the variable dimension in reactive power optimization, greatly improves the calculation efficiency, and at the same time improves the voltage stability, reduces the line loss and fully utilizes the reactive power margin of wind turbines in the scenario of high new energy penetration rate, and has strong applicability and superiority.

Description

Technical Field

[0001] The invention belongs to the technical field of power system planning, and particularly relates to a reactive power optimization method and system for a power grid with wind turbines based on voltage weak point identification. Background Art

[0002] The large-scale access of new energy wind turbines to the power system is becoming more and more common. With the access of large-scale new energy wind turbines, the original system network power flow distribution has changed, and due to the randomness and uncertainty of the wind turbine output, it will bring certain hidden dangers to the stability of the voltage in the system, thus affecting the safe operation of the overall power grid. Therefore, in order to improve the voltage stability level of the power grid, it is very necessary to optimize the allocation of reactive power resources, and it is of great significance to establish a voltage reactive power optimization model applicable to the power grid.

[0003] At present, most methods directly perform reactive power optimization by using reactive power compensation equipment after new energy is connected to the power grid, directly adjust the voltage by using reactive power compensation equipment, ignoring the regulation of using the reactive power margin of new energy itself to participate in reactive power optimization, and involving many nodes where reactive power compensation equipment is connected, with a large number of connected reactive power equipment, directly increasing the variable dimension in the optimization solution, and the result is easy to fall into local convergence, resulting in poor final optimization effect, and greatly increasing the investment cost of reactive power compensation equipment. Summary of the Invention

[0004] Aiming at the problem of node voltage fluctuation after a doubly-fed wind turbine is connected to the power grid, the invention proposes a reactive power optimization method for a power grid with wind turbines based on voltage weak point identification.

[0005] A reactive power optimization method for a power grid with wind turbines based on voltage weak point identification includes the following steps:

[0006] Connect multiple wind farm stations composed of doubly-fed wind turbines to the power grid, judge the node voltage change index of each connected node, and obtain the voltage weak points after the wind farm stations are connected to the power grid;

[0007] Take the voltage weak points as the compensation nodes for the access of reactive power equipment, construct a reactive power optimization model, and the reactive power optimization model takes the minimum node voltage deviation, the minimum line loss, and the minimum total investment cost of the reactive power equipment invested in the compensation nodes in the power grid system as the objective function, and at the same time satisfies the power flow equation constraint and the inequality constraints of the generator terminal voltage, the on-load tap-changer of the transformer, the number of reactive power equipment invested, and the reactive power regulation range of the wind farm station;

[0008] Use an intelligent optimization algorithm to iteratively update the control variables, calculate the solution that satisfies the reactive power optimization model, and output the optimal control variables.

[0009] In the above reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, when the doubly-fed induction generator (DFIG) is connected to the grid side and operates normally, the maximum reactive power Q absorbed by the DFIG min is the sum of the maximum reactive power Q absorbed by the stator side smin and the maximum reactive power Q absorbed by the grid-side converter gmin . The maximum reactive power Q generated by the DFIG max is the sum of the maximum reactive power Q generated by the stator side smax and the maximum reactive power Q generated by the grid-side converter gmax .

[0010] In the above reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, the complete PV curve of each node in the power grid is obtained by the continuation power flow method, the voltage amplitude of each node under the critical state of power transmission is determined, and the node voltage change index ΔV i is constructed. By judging the node voltage change index of each node, a voltage weak point set composed of voltage weak points after several wind farms are connected to the power grid is obtained.

[0011] In the above reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, the control variables are the generator terminal voltage, the on-load tap changer of the transformer, the number of reactive power equipment connected to the compensation node, and the reactive power margin of the wind farm participating in the optimization. An intelligent optimization algorithm is used to iteratively update the above variables, and the solution that satisfies the objective function and the equality and inequality constraint conditions in the reactive power optimization model is calculated.

[0012] In the above reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, the reactive power optimization model is solved according to the particle swarm optimization algorithm with improved inertia weight. The initial conditions in the algorithm are input, which include the number of iterations m, the population size s, the speed update parameters c1 and c2, and the inertia weight parameter w. The solution that satisfies the objective function, the equality constraint conditions, and the inequality constraint conditions is obtained through iterative calculation.

[0013] In the above reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, when the DFIG connected to the power grid operates normally, its reactive power range Q is

[0014]

[0015] In Equation (1), Q gmin is the maximum reactive power absorbed by the grid-side converter of the DFIG; Q gmax is the maximum reactive power generated by the grid-side converter of the DFIG; Q min is the maximum reactive power absorbed by the DFIG; Q max is the maximum reactive power generated by the DFIG.

[0016] In the above reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, the continuous power flow method is adopted and combined with the node voltage change index ΔV i The voltage weak nodes after the wind farm is connected to the power grid are judged. It is characterized in that: the PV curves corresponding to each node are obtained by the continuous power flow method, so as to determine the voltage amplitude of each node under the critical state of power transmission, and the node voltage change index ΔV is constructed i For

[0017]

[0018] In formula (2), V i0 is the initial voltage of node i after the wind farm is connected to the power grid system; V cri is the voltage corresponding to node i under the critical state. After the wind farm is connected to the power grid, the node voltage change index ΔV i can reflect the influence of the change of load or branch transmission power on the voltage of this node. The larger the node voltage change index, the more vulnerable the node voltage is here

[0019] In the above reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, the objective function is

[0020]

[0021] In formula (3), M is the number of system nodes; v is the node number; U v is the actual voltage value of the current node; U N is the rated voltage value of the node; V i , V j and θ ij are the voltage amplitudes of nodes i and j and the phase angle difference between the two nodes respectively; N L is the set of all branches in the system; w is the reactive power compensation node number, m is the cost of each group of capacitors, and C is the number of capacitor banks connected to the reactive power compensation node

[0022] In the above reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, the equality constraint conditions and inequality constraint conditions are

[0023]

[0024]

[0025]

[0026] In formulas (4) to (6), P i , Q i are the active power and reactive power of node i, G ij , Bij is the conductance and susceptance between node i and node j, and U i 、U j are the voltage values of node i and node j; U Gi is the terminal voltage of the generator at the i-th node, and T i is the tap position of the on-load tap-changing transformer, and Q Ci is the number of switched shunt capacitors for reactive power compensation; Q Gi 、Q Fi are the reactive power magnitudes of the generator and the doubly-fed wind turbine.

[0027] A reactive power optimization system for a power grid with wind turbines based on voltage weak point identification, including

[0028] The first module: Connect multiple wind farm stations composed of doubly-fed wind turbines to the power grid. The first module judges the node voltage change index of each connected node to obtain the voltage weak points after the wind farm stations are connected to the power grid;

[0029] The second module: Used to take the voltage weak points as the compensation nodes for connecting reactive power devices, and construct a reactive power optimization model. The reactive power optimization model takes the minimum node voltage deviation, minimum line loss, and minimum total investment cost of the reactive power devices connected to the compensation nodes in the power grid system as the objective function, and at the same time satisfies the power flow equation constraints and the inequality constraints of the generator terminal voltage, on-load tap-changing transformer tap, the number of reactive power devices connected, and the reactive power regulation range of the wind farm stations;

[0030] The third module: Used to iteratively update the control variables by using an intelligent optimization algorithm, calculate the solution that satisfies the reactive power optimization model, and output the optimal control variables.

[0031] The present invention proposes to identify the weak voltage nodes after new energy wind turbines are connected to the power system based on the continuous power flow method. The continuous power flow method calculates the voltage amplitude of each node in the power grid system at the critical state, uses the node voltage change index to judge the voltage weak nodes in the system, and takes this node as the connection point of the reactive power compensation device. Then, taking the system voltage deviation, line loss, and reactive power device investment cost as the objective function, the reactive power margin of the wind turbine is used to participate in the comprehensive reactive power optimization in the optimization to tap the output capacity of the wind turbine. While adjusting the power grid voltage, the utilization rate of the new energy wind turbine is improved, reflecting certain superiority.

[0032] The present invention mines the influencing factors of the regulation ability based on the reactive power regulation model of a doubly-fed wind turbine, releases the reactive power margin of the wind turbine to participate in the system reactive power optimization, improves the utilization rate of the overall output of the wind turbine, reduces the number of reactive power equipment connected to the grid system to participate in the voltage reactive power optimization, saves the investment cost of the reactive power equipment, and uses the continuation power flow method to identify the voltage weak nodes after the wind turbine is connected to the grid, and compensates the reactive power equipment for the identified nodes, greatly reducing the variable dimension in the optimization solution, reducing the redundant workload, and greatly improving the voltage reactive power optimization efficiency. Description of the Drawings

[0033] Figure 1 Power conversion model diagram of a doubly-fed wind turbine.

[0034] Figure 2 Diagram of a doubly-fed wind turbine connected to the IEEE 30-node system.

[0035] Figure 3 Voltage change diagram before and after the wind turbine is connected to the grid.

[0036] Figure 4 Continuation power flow method combined with node voltage change index diagram.

[0037] Figure 5 Complete PV curve of voltage weak nodes.

[0038] Figure 6 Flow chart of obtaining voltage weak nodes and improving particle swarm optimization algorithm.

[0039] Figure 7 System voltage change diagram before and after the wind turbine is connected and before and after optimization. Detailed Implementation Modes

[0040] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the following further details the present invention in combination with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0041] The following are the preferred embodiments of the present invention, and further illustrate the specific applications of the present invention in combination with the accompanying drawings.

[0042] The specific implementation mode of the present invention relates to a reactive power optimization method for a power grid with wind turbines based on the identification of voltage weak points, specifically as follows:

[0043] Step 1: Obtain the power network structure parameters and electrical parameters. The structure parameters include the grid adjacency matrix and line lengths; the electrical parameters include network power flow data, power supply capacity, load data, line impedance parameters, and build a power grid system with wind turbine access. Build an improved IEEE 30-node power grid system with wind turbine access as shown in the appendix Figure 2 as shown

[0044] The improved IEEE 30-node power grid system contains 41 branches. There are originally 6 conventional thermal power units installed in the system. Keep the G1 unit and remove the other 5 conventional thermal power units. Install doubly-fed wind turbine units at nodes 3, 10, 12, 15, and 25 respectively. The base power of the system is 100 MW, the total access capacity of the 5 wind turbines is 128 MW, and the wind power penetration rate of the system after the wind turbines are connected is 40%.

[0045] Step 2: Calculate the reactive power regulation range of the wind turbines connected to the power grid according to the Figure 1 doubly-fed wind turbine power conversion model

[0046] The power transmission and conversion model of the doubly-fed wind turbine is as shown in the appendix Figure 1 as shown. For a conventional doubly-fed wind turbine, the reactive power range on the stator side is

[0047] Q smin ≤Q s ≤Q smax (1)

[0048]

[0049] where Q s is the reactive power generated by the stator side of the doubly-fed wind turbine; Q smin is the maximum reactive power absorbed by the stator side of the doubly-fed wind turbine; Q smax is the maximum reactive power generated by the stator side of the doubly-fed wind turbine; Q exi is the internal excitation reactive power of the doubly-fed wind turbine. During normal operation, the terminal voltage of the doubly-fed wind turbine is approximately constant, but as the active power output to the power grid side increases, the adjustable reactive power inside the doubly-fed wind turbine will continuously decrease

[0050] When the doubly-fed wind turbine is connected to the power grid side and operates normally, its reactive power output range is directly related to the reactive power regulation capabilities of the stator side and the grid side converters. When the doubly-fed wind turbine operates normally, the active power P g absorbed by the grid side converter, the active power P r absorbed by the rotor side, and the active power P s generated by the stator side satisfy the relationship

[0051] P g =P r =sP s (3)

[0052] Where s is the slip rate on the rotor side of the doubly-fed wind turbine. Therefore, when the doubly-fed wind turbine is operating normally, the reactive power regulation range of its grid-side converter is

[0053]

[0054]

[0055] Where S g is the rated capacity of the grid-side converter of the doubly-fed wind turbine; Q g is the reactive power absorbed by the grid-side converter of the doubly-fed wind turbine.

[0056] To sum up, when the doubly-fed wind turbine is operating normally after being connected to the grid, the reactive power regulation range is jointly determined by the reactive power range on the stator side and the reactive power range of the grid-side converter. Therefore, the reactive power regulation range of the doubly-fed wind turbine can be obtained as

[0057]

[0058]

[0059] Where Q gmin is the maximum reactive power absorbed by the grid-side converter of the doubly-fed wind turbine; Q gmax is the maximum reactive power generated by the grid-side converter of the doubly-fed wind turbine; Q min is the maximum reactive power absorbed by the doubly-fed wind turbine; Q max is the maximum reactive power generated by the doubly-fed wind turbine.

[0060] When the doubly-fed wind turbine is operating normally after being connected to the grid, the reactive power regulation range of the doubly-fed wind turbine connected to the grid can be obtained as shown in Table 1 below.

[0061] Table 1 Reactive Power Regulation Range of Wind Turbines Connected to IEEE 30-Node System

[0062]

[0063]

[0064] Step 3: After a large number of wind turbines are connected to the power system, due to the randomness and volatility of the output power, it will cause large fluctuations in the node voltages in the power grid at a high wind power penetration rate, which will further affect the safe and stable operation of the power grid. The voltage changes in the IEEE 30-node system before and after the wind power connection are as shown in the appendix Figure 3 shown. First, the continuous power flow method needs to be used to calculate the PV curves corresponding to each node in the power grid system. Secondly, the node voltage change indexes are calculated under the critical state of the PV curve, and the weak voltage nodes are identified according to the node voltage change indexes.

[0065] The continuous power flow method is used to draw the PV curve of each node voltage and calculate the voltage change index of each node under the critical state. The basic model of the continuous power flow method is the extended power flow equation. By analyzing various state indicators of the system under the critical operating state, it is judged whether the current state is stable. The operating state when the transmission power of a branch reaches the maximum transmission power is the critical operating state.

[0066] Assume that the n-dimensional power flow equation with parameters in the system is

[0067] f(x,λ)=0 (8)

[0068] Where x is the voltage amplitude and phase angle of the node in the system, and λ is the load growth factor.

[0069] When the general power flow calculation method calculates the critical point, the Jacobian matrix at the critical point will be singular, so that the entire power flow calculation equation will not converge. In the continuous power flow method, the input load is introduced to increase the parameters to overcome the singular problem of the Jacobian matrix, thereby obtaining a complete PV curve for the node. The continuous power flow method consists of four parts: parameterization, prediction, step size and correction.

[0070] 1) Parameterization

[0071] Parameterization is to introduce a parameter λ to characterize the load change under the premise of the original power flow equations to change the structure of the Jacobian matrix to avoid the Jacobian matrix singularity problem when calculating to the critical point. In the present invention, the local parameterization is selected as

[0072] λ-λ (t) =0 (9)

[0073] The introduction of parameter λ increases the dimension of the power flow equations by one, and equations (14) and (15) can be solved simultaneously.

[0074] 2) Prediction

[0075] The prediction is to predict the next solution along the growth direction of the load change parameter λ, where the quality of the prediction value directly affects the efficiency of subsequent calculations. Generally, the more accurate the prediction value is, the fewer the number of iterations of the overall calculation will be, and vice versa, it may even lead to divergence.

[0076] Commonly used prediction methods are the tangent method and the secant method in the linear prediction method. In the prediction process, the tangent method prediction requires a tidal current solution, and the secant method prediction requires at least two tidal current solutions. Based on this characteristic, this paper uses the tangent method to obtain another accurate tidal current value in the first step of prediction. After obtaining two tidal current solutions, it switches to the secant method prediction.

[0077] 3) Step length control and correction

[0078] In the present invention, a dynamic step size adjustment is selected. A large step size is selected when the PV curve is far from the critical point, and a small step size is selected near the critical point for solution.

[0079] The calibration operation uses the predicted value as the initial point to obtain the actual value through calculation. In this paper, an improvement is made based on the classical Newton-Raphson method, and the local calibration method is used for iterative calculation. After adding an equation, it becomes

[0080]

[0081] In the formula, V i (t) is the predicted value of the voltage amplitude. The Newton-Raphson method is used for iterative solution, and the iterative equation is

[0082]

[0083] [Δx,Δλ] is obtained according to the above formula T and then substituted into the correction formula as

[0084]

[0085] Thus, the correction values [x,λ] can be obtained T .

[0086] In summary, the voltage change indexes of each node in the improved IEEE 30-node power grid system under the critical state are calculated as shown in the appendix Figure 4 As shown, the results show that nodes 5, 18, 29, and 30 are voltage weak nodes, that is, when the load in the system reaches the maximum, the voltage change index of the nodes is the largest in the system. The complete PV curves corresponding to the voltage weak nodes are shown in the appendix Figure 5 as shown.

[0087] Step 4: Construct a reactive power optimization model with the voltage weak point as the compensation node and use the improved weight particle swarm optimization algorithm for solution. Under the premise of a high wind power penetration rate of 40%, the generator terminal voltage, the reactive power regulation ability of the wind turbine, the tap ratio regulation of the on-load transformer, and the reactive power compensation equipment are placed at the voltage weak nodes of the load to carry out reactive power optimization to improve the voltage stability of the system. The generator terminal voltage, the on-load adjustable transformer, the reactive power compensation equipment, and the reactive power regulation power of the fan in the system are used as the control variables to be optimized. There are thermal power generators and wind turbines at nodes 1, 3, 10, 12, 15, and 25 of the system, and the variable range of the terminal voltage is 0.9 - 1.1 pu; on-load tap-changing transformers are installed at branches 6-10, 6-9, 4-12, and 27-28, and their regulation range is ±8×1.25%; there are 5 groups of capacitors for reactive power compensation at nodes 18, 29, and 30 respectively, and the compensation capacity of each group of capacitors is 1.5 Mvar, and the cost of each group of capacitors is set to 1.

[0088] The comparison of the control variables before and after optimization is shown in Table 2. The target results of the reactive power optimization are shown in Table 3. The changes in the grid node voltages before and after optimization are shown in the appendix Figure 7 as follows.

[0089] Table 2 Results of Optimized Control Variables

[0090]

[0091] Table 3 Target Results of Reactive Power Optimization

[0092]

[0093] It can be seen that when the improved weighted particle swarm optimization algorithm is applied to the reactive power optimization, its fitness value does not fall into a local optimal cycle, and it drops faster and has higher convergence than other optimization algorithms. This shows that the optimization algorithm has certain superiority for the reactive power optimization calculation in the present invention. After the wind turbines replace the original thermal power units in the system, the node voltages of the system drop severely. With the comprehensive optimization of the reactive power compensation for the weak voltage nodes, the reactive power margin of the wind turbines, the terminal voltage of the generators, and the transformer tap positions, the voltage level of the system is significantly improved, ensuring the safe and stable operation of the system.

Claims

1. A reactive power optimization method for a power grid with wind turbines based on voltage weak point identification, characterized in that It includes the following steps: Connect multiple wind farm stations composed of doubly-fed wind turbines to the power grid, judge the node voltage change index of each connected node, and obtain the voltage weak points after the wind farm stations are connected to the power grid; Take the voltage weak points as the compensation nodes for reactive power equipment access, and construct a reactive power optimization model. The reactive power optimization model takes the minimum node voltage deviation, minimum line loss, and minimum total investment cost of the reactive power equipment invested at the compensation nodes in the power grid system as the objective function, and at the same time satisfies the power flow equality constraint and the inequality constraints of the generator terminal voltage, on-load tap-changer of the transformer, the number of reactive power equipment invested, and the reactive power regulation range of the wind farm stations; Use an intelligent optimization algorithm to iteratively update the control variables, calculate the solution that satisfies the reactive power optimization model, and output the optimal control variables; Obtain the complete PV curves of each node in the power grid through the continuation power flow method, determine the voltage amplitude of each node under the critical state of power transmission, and construct the node voltage change index ΔV i , judge the node voltage change index of each node, and obtain a voltage weak point set composed of voltage weak points after several wind farms are connected to the power grid; The objective function is In Equation (3), M is the number of system nodes; v is the node number; U v is the actual voltage value of the current node; U N is the rated voltage value of the node; V i 、V j and θ ij are the voltage magnitudes of nodes i and j and the phase angle difference between the two nodes, respectively; N L is the set of all branches in the system; w is the number of the reactive power compensation node, m is the cost of each capacitor bank, and C is the number of capacitor banks connected to the reactive power compensation node.

2. A reactive power optimization method for a power grid with wind turbines based on voltage weak point identification according to claim 1, wherein, When the doubly-fed wind turbine is operating normally on the grid side, the maximum reactive power Q absorbed by the doubly-fed wind turbine min is the sum of the maximum reactive power Q smin absorbed by the stator side and the maximum reactive power Q gmin absorbed by the grid-side converter. The maximum reactive power Q max generated by the doubly-fed wind turbine smax is the sum of the maximum reactive power Q gmax generated by the stator side and the maximum reactive power Q generated by the grid-side converter.

3. A reactive power optimization method for a power grid with wind turbines based on voltage weak point identification according to claim 1, characterized in that The control variables are the generator terminal voltage, the on-load transformer tap, the number of reactive power equipment connected at the compensation nodes, and the reactive power margin of the wind farm stations participating in the optimization. Use an intelligent optimization algorithm to iteratively update the above variables, and calculate the solution that satisfies the objective function and the equality and inequality constraint conditions in the reactive power optimization model.

4. A reactive power optimization method for a fan-integrated power grid based on voltage weak point identification according to claim 1, characterized in that Solve the constructed reactive power optimization model according to the particle swarm optimization algorithm with improved inertia weight, and input the initial conditions in the algorithm, which include the number of iterations m, the population size s, the speed update parameters c1 and c2, and the inertia weight parameter w, and iteratively calculate to obtain the solution that satisfies the objective function, equality constraint conditions, and inequality constraint conditions.

5. A reactive power optimization method for a power grid with wind turbines based on voltage weak point identification according to claim 1, characterized in that, When the doubly-fed wind turbine operates normally after being connected to the power grid, its reactive power range Q is In formula (1), Q gmin is the maximum reactive power absorbed by the grid-side converter of the doubly-fed wind turbine; Q gmax is the maximum reactive power generated by the grid-side converter of the doubly-fed wind turbine; Q min is the maximum reactive power absorbed by the doubly-fed wind turbine; Q max is the maximum reactive power generated by the doubly-fed wind turbine.

6. A reactive power optimization method for a power grid with wind turbines based on voltage weak point identification according to claim 1, characterized in that, Using the continuation power flow method and combining with the node voltage change index ΔV i Judge the weak voltage nodes after the wind farm is connected to the power grid. Obtain the PV curves corresponding to each node through the continuation power flow method, so as to determine the voltage amplitude of each node under the critical state of power transmission, and construct the node voltage change index ΔV i To V in Equation (2) i0 is the initial voltage of Node i after the wind farm is connected to the power grid system; V cri is the voltage corresponding to Node i in the critical state. After the wind farm is connected to the power grid, the node voltage change index ΔV i can reflect the impact of the change in load or branch transmission power on the voltage of this node. The larger the node voltage change index, the more vulnerable the node voltage is here.

7. A reactive power optimization method for a power grid with wind turbines based on voltage weak point identification according to claim 1, characterized in that, The equality constraint conditions and inequality constraint conditions are P in equations (4) to (6) i and Q i are the active power and reactive power of node i, G ij and B ij are the conductance and susceptance between node i and node j, U i and U j are the voltage values of node i and node j; U Gi is the terminal voltage of the generator at the i-th node, T i is the tap position of the on-load tap-changer transformer, Q Ci is the number of switched shunt capacitors for reactive power compensation; Q Gi 、Q Fi are the reactive power magnitudes of the generator and the doubly-fed wind turbine.

8. A reactive power optimization system for a power grid with wind turbines based on voltage weak point identification, characterized in that, It includes The first module: Connect multiple wind farm stations composed of doubly-fed wind turbines to the power grid. The first module judges the node voltage change index of each connected node and obtains the voltage weak points after the wind farm stations are connected to the power grid; The second module: Used to take the voltage weak points as the compensation nodes for reactive power equipment access and construct a reactive power optimization model. The reactive power optimization model takes the minimum node voltage deviation, minimum line loss, and minimum total investment cost of the reactive power equipment invested at the compensation nodes in the power grid system as the objective function, and at the same time satisfies the power flow equality constraint and the inequality constraints of the generator terminal voltage, on-load tap-changer of the transformer, the number of reactive power equipment invested, and the reactive power regulation range of the wind farm stations; The third module: Used to use an intelligent optimization algorithm to iteratively update the control variables, calculate the solution that satisfies the reactive power optimization model, and output the optimal control variables; Obtain the complete PV curves of each node in the power grid by the continuation power flow method, determine the voltage amplitude of each node under the critical state of power transmission, and construct the node voltage change index ΔV i , judge the node voltage change index of each node, and obtain a voltage weak point set composed of voltage weak points after several wind farms are connected to the power grid; The objective function is In Equation (3), M is the number of system nodes; v is the node number; U v is the actual voltage value of the current node; U N is the rated voltage value of the node; V i 、V j and θ ij are the voltage magnitudes of nodes i and j, respectively, and the phase angle difference between the two nodes; N L is the set of all branches in the system; w is the number of the reactive power compensation node, m is the cost of each capacitor bank, and C is the number of capacitor banks connected to the reactive power compensation node.

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