Security and stability analysis method of new energy power system based on Lyapunov function

Abstract

The present invention discloses a safety and stability analysis method for a new energy power system based on a Lyapunov function, the method comprising the following steps: obtaining the voltage at a new energy grid connection point, the voltage phase angle at a new energy grid connection point, the internal potential of a synchronous machine, the line susceptance and the rotor position angle of a synchronous machine of the new energy power system to obtain the output power of the synchronous machine; based on the new energy power system, obtaining the synchronous machine rotor motion equation according to the synchronous machine output power; constructing the Lyapunov function of the synchronous machine based on the new energy power system according to the synchronous machine rotor motion equation; obtaining the stable domain boundary of the synchronous machine with respect to the state variable according to the Lyapunov function; based on the stable domain boundary, judging the transient stability of the synchronous machine according to the real-time numerical value of the state variable after the fault. The safety and stability analysis method for a new energy power system based on a Lyapunov function provided by the present invention has low construction difficulty, is universal for nonlinear systems of different forms, and has fast and accurate transient stability evaluation.

Description

Technical Field

[0001] The present invention relates to the technical field of safety analysis of new energy stations, and in particular to a safety and stability analysis method for a new energy power system based on a Lyapunov function. Background Art

[0002] Since the goal of "carbon peak and carbon neutrality" was proposed, the construction of a new power system dominated by clean energy has become the main development direction of China's future energy and electricity, and a high proportion of new energy access will become the basic feature and development form of the modern power system. However, the increasing load demand, operating conditions closer to the system limit, larger interconnected power grids and more new energy units connected by power electronic components have made the modern power system more complex, and the operation of the power system is facing more severe challenges. In order to provide safe and reliable power services, the stability of these modern power systems and power supply equipment must be maintained. The growth and evolution of the scale of modern power systems and the near-limit operating conditions of power systems have led to different forms of instability problems. Therefore, the stability of modern power systems has become increasingly important for the safe operation of power grids.

[0003] The transient stability of the power system, also known as the "first swing" stability, refers to the ability of each synchronous generator to maintain synchronous rotation and convert to a new state or restore to the original stable working state after the power system suffers a large disturbance. Transient instability is also the main factor leading to large-scale power outages. The occurrence of large-scale power system power outages will seriously affect people's production and life and cause huge economic losses. The Lyapunov function construction method applied to traditional power systems is only applicable to specified models. It mainly uses energy functions and square sum planning methods. The square sum planning method is limited to polynomial systems. For non-polynomial systems, it is necessary to first use Taylor expansion to approximate the motion equations, and then calculate the stability domain based on the approximate polynomial equations. Compared with traditional power systems, power systems with new energy access have more complex characteristics. The Lyapunov function construction method applied to traditional power systems has the problem of non-integrability for complex systems, making it difficult to obtain energy functions, and cannot handle nonlinear systems of different forms. There is no universal Lyapunov function construction method for power systems with new energy access. Summary of the invention

[0004] In order to solve the above problems in the prior art, the present invention provides a new energy power system safety and stability analysis method based on Lyapunov function, which has low construction difficulty, is universal for different forms of nonlinear systems, and has fast and accurate transient stability assessment.

[0005] In order to achieve the above-mentioned invention object, the present invention provides a new energy power system security and stability analysis method based on Lyapunov function, comprising the following steps:

[0006] Obtain the voltage at the grid connection point of the new energy power system, the voltage phase angle at the grid connection point of the new energy power system, the internal potential of the synchronous machine, the line susceptance and the rotor position angle of the synchronous machine;

[0007] The output power of the synchronous machine is obtained according to the voltage at the new energy grid connection point, the voltage phase angle at the new energy grid connection point, the internal potential of the synchronous machine, the line susceptance and the synchronous machine rotor position angle; the output power of the synchronous machine is:

[0008] ;

[0009] In the formula, For the Output power of synchronous machine, For the The potential inside the synchronous machine, is the current synchronous machine number, is the synchronous machine serial number, is the total number of synchronous machines, For the The potential inside the synchronous machine, For the The first synchronous machine and the The line susceptance between the synchronous machines, For the The synchronous machine rotor position angle, For the The synchronous machine rotor position angle, It is the serial number of the new energy grid connection point. is the total number of new energy grid-connected points, For the Voltage of each new energy grid connection point, For the The first synchronous machine and the The line impedance between the new energy grid connection points is For the Voltage phase angle of each new energy grid connection point;

[0010] Based on the new energy power system, obtaining the synchronous machine inertia constant, the synchronous machine prime mover power and the synchronous machine inertia center time constant;

[0011] Obtaining a synchronous machine rotor motion equation according to the synchronous machine inertia constant, the synchronous machine prime mover power, the synchronous machine inertia center time constant and the synchronous machine output power, wherein the state variables of the synchronous machine rotor motion equation are the synchronous machine rotor position angle and the synchronous machine rotor angular velocity;

[0012] Constructing a Lyapunov function of a synchronous machine based on the new energy power system according to the synchronous machine rotor motion equation;

[0013] Obtaining the stability domain boundary of the synchronous machine with respect to the state variable according to the Lyapunov function;

[0014] Based on the stability region boundary, the transient stability of the synchronous machine is determined according to the real-time value of the post-fault state variable.

[0015] Furthermore, the voltage of the new energy grid connection point is:

[0016] ;

[0017] The voltage phase angle of the new energy grid connection point is:

[0018] ;

[0019] In the formula, For the Voltage of each new energy grid connection point, For the A new energy grid-connected point self-reactor, is the synchronous machine serial number, is the total number of synchronous machines, For the The potential inside the synchronous machine, For the The first synchronous machine and the The reactance between the new energy grid connection points, For the The synchronous machine rotor position angle, For the The new energy grid-connected point injects current, For the The voltage phase angle of each new energy grid connection point.

[0020] Furthermore, the synchronous machine rotor motion equation is:

[0021] ;

[0022] Where:

[0023] ;

[0024] ;

[0025] In the formula, For the The synchronous machine rotor position angle, For the The synchronous machine rotor angular velocity, For the The inertia time constant of a synchronous machine, For the The power of the synchronous machine prime mover, For the Output power of synchronous machine, for The time constant of the center of inertia of a synchronous machine, for The inertia center power of synchronous machine, is the current synchronous machine number, is the total number of synchronous machines.

[0026] Furthermore, the steps of constructing the Lyapunov function are:

[0027] Based on the synchronous machine rotor motion equation, a sample set is acquired in a preset area, where the sample set is a set of values ​​of the state variables;

[0028] Initialize the parameters and number of iterations of the neural network;

[0029] Obtaining an output scalar function based on the sample set and the parameters of the neural network;

[0030] Obtaining an output risk function according to the sample set, the parameters of the neural network, the output scalar function and the equation of motion;

[0031] Inputting or setting the operating parameters of the neural network, the operating parameters including input dimension, output dimension, hidden layer dimension, learning rate and maximum number of iterations; obtaining the input dimension according to the synchronous machine rotor motion equation, and obtaining the output dimension according to the output scalar function;

[0032] Obtaining an activation function of the neural network;

[0033] Running the neural network based on the operating parameters, the parameters of the neural network, the number of iterations, the activation function, the output scalar function, and the output risk function to obtain an output function;

[0034] A Lyapunov function of a synchronous machine based on the new energy power system is obtained according to the output function.

[0035] Furthermore, the operation steps of the neural network are:

[0036] Step 1: Judgement Is it established? In the formula, is the number of iterations, is the maximum number of iterations:

[0037] If not, modify the preset area or the sample set;

[0038] If established, the neural network is run;

[0039] Step 2: updating the parameters of the neural network according to the output risk function, and obtaining the output function according to the output scalar function;

[0040] Step 3: Determine whether the output function meets the output verification condition:

[0041] If the output function does not satisfy the output verification condition, then , repeat step 1 to step 2;

[0042] If the output function satisfies the output verification condition, then the output function is the Lyapunov function.

[0043] Furthermore, the output risk function is:

[0044] ;

[0045] Where:

[0046] ,

[0047] ;

[0048] In the formula, is the output risk function, is the value of the state variable, are the parameters of the neural network, is the total number of samples, is the sample serial number, For the The value of the sample state variable, is the function corresponding to the synchronous machine rotor motion equation, For about The partial differential of represents transpose, for The constraint function is for The constraint function is is the output scalar function, is the margin distance of the output function from the origin, is the margin distance of the derivative of the output function from the origin, ≥0, ≥0, is the output function, is the derivative of the output function.

[0049] Furthermore, the step of determining whether the output function satisfies the output verification condition is as follows:

[0050] Based on the solver, a verification function is obtained according to the sample set and the output function, wherein the verification function is:

[0051] ;

[0052] Where: To verify the function, is the total number of samples, is the sample serial number, For the The value of the sample state variable, To limit the small constant parameter that can tolerate numerical errors, is the value of the state variable, is the output function, is the derivative of the output function, , is the set of positive rational numbers;

[0053] Using the solver to solve the verification function and determine whether the verification function is established;

[0054] If the verification function does not hold, then the output function does not satisfy the output verification condition;

[0055] If the verification function holds, the output function satisfies the output verification condition.

[0056] Furthermore, when the verification function does not hold, the state variable value of the output function that does not satisfy the output verification condition is obtained according to the verification function, the state variable value of the output function that does not satisfy the output verification condition is added to the sample set, and the sample set is updated; and steps 1 to 2 are repeated based on the updated sample set.

[0057] Furthermore, the output verification condition is:

[0058] ,

[0059] ;

[0060] In the formula, is the output function, is the value of the state variable, For the preset area, is the derivative of the output function.

[0061] Furthermore, the hidden layer dimension is 7.

[0062] The beneficial effects of the present invention are:

[0063] 1. The present invention calculates the output power of the synchronous machine according to the voltage of the new energy grid connection point, the voltage phase angle of the new energy grid connection point, the internal potential of the synchronous machine, the line susceptance and the synchronous machine rotor position angle in the new energy power system, and obtains the synchronous machine rotor motion equation based on the output power of the synchronous machine to construct the Lyapunov function, which linearizes the complex nonlinear system and reduces the difficulty of constructing the Lyapunov function. It is a general construction method of the Lyapunov function of power systems with different forms of new energy access;

[0064] 2. Based on the stability domain boundary determined by the Lyapunov function constructed by the present invention, by observing the real-time values ​​of the synchronous machine rotor position angle and the synchronous machine rotor angular velocity in the new energy power system after a fault, and judging whether these two state variables are within the stability domain boundary to judge the transient stability of the synchronous machine, and then conducting a safety and stability analysis of the new energy power system, a fast and accurate transient stability assessment of the new energy power system is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Schematic diagram of the steps of the analysis method of the present invention;

[0066] Figure 2 A schematic diagram of the process of constructing a Lyapunov function in the present invention;

[0067] Figure 3 A schematic diagram of the topological network structure of a three-machine nine-node new energy power system in an example of the present invention;

[0068] Figure 4 is the Lyapunov function of the synchronous machine G1 under working condition 1 in the example of the present invention;

[0069] Figure 5 is the derivative of the Lyapunov function of the synchronous machine G1 under working condition 1 in the example of the present invention;

[0070] Figure 6 is the Lyapunov function of the synchronous machine G1 under working condition 2 in the example of the present invention;

[0071] Figure 7 is the derivative of the Lyapunov function of the synchronous machine G1 under working condition 2 in the example of the present invention;

[0072] Figure 8 Schematic diagram of the stability domain boundary under working condition 2 in an example of the present invention. DETAILED DESCRIPTION

[0073] Online transient stability assessment is conducive to taking timely measures to maintain the stability of the power system, and is of great significance for the forward-looking scheduling and planning of the power system. When phasor measurement units are widely deployed in the power grid, a large amount of power grid measurement data can be obtained synchronously to capture the state and dynamics of the entire system in real time. Based on a large amount of power grid measurement data, data-driven transient stability assessment is a fast and efficient way. In particular, with the help of advanced artificial intelligence methods, the potential relationship between the operating state variables and the stability state of the power system under study can be fully revealed. As a data-driven stability judgment, these relationships can be used to achieve fast and accurate transient stability assessment.

[0074] The existing technology is limited in constructing the Lyapunov function of synchronous machines in renewable energy power systems. In order to maintain the safe and stable operation of the power supply system and prevent large-scale power outages, a rapid and accurate transient stability assessment method is urgently needed, which is suitable for the safety and stability analysis of power systems with renewable energy access, and provides information guarantee for the effective implementation of prevention and emergency control measures for transient stability operation of renewable energy power systems after faults occur.

[0075] In order to clearly illustrate the technical features of this solution, this solution is described below through a specific implementation method.

[0076] The embodiment of the present invention provides a new energy power system security and stability analysis method based on Lyapunov function. Specifically, the new energy power system has a total of Synchronous machine and If there are new energy grid-connected points, The output power of a synchronous machine is as follows:

[0077] (1)

[0078] In the formula, For the Output power of synchronous machine, represents the real part, For the The derivative of the potential inside a synchronous machine, is the current synchronous machine number, is the synchronous machine serial number, is the total number of synchronous machines, For the The conjugate of the current injected by the synchronous machine, For the The first synchronous machine and the The conjugate of the admittance between the synchronous machines, For the The phasor of the derivative of the potential in a synchronous machine, It is the serial number of the new energy grid connection point. is the total number of new energy grid-connected points, For the The first synchronous machine and the The conjugate of mutual admittance between the new energy grid connection points, For the The phasor of the derivative of the voltage at the grid connection point of a new energy source;

[0079] When the line resistance is ignored, equation (1) can be expressed as equation (2):

[0080] (2)

[0081] In the formula, For the Output power of synchronous machine, For the The potential inside the synchronous machine, is the current synchronous machine number, is the synchronous machine serial number, is the total number of synchronous machines, For the The potential inside the synchronous machine, For the The first synchronous machine and the The line susceptance between the synchronous machines, For the The synchronous machine rotor position angle, For the The synchronous machine rotor position angle, It is the serial number of the new energy grid connection point. is the total number of new energy grid-connected points, For the Voltage of each new energy grid connection point, For the The first synchronous machine and the The line impedance between the new energy grid connection points is For the Voltage phase angle of each new energy grid connection point;

[0082] Therefore, based on formula (2), after obtaining the voltage of the new energy grid connection point, the voltage phase angle of the new energy grid connection point, the internal potential of the synchronous machine, the line susceptance and the synchronous machine rotor position angle of the new energy power system, the output power of the synchronous machine can be calculated according to formula (1); the complex nonlinear system is linearized to reduce the difficulty of constructing the Lyapunov function suitable for the new energy power system;

[0083] On the basis of formula (2), based on the new energy power system, the synchronous machine rotor motion equation can be obtained by obtaining the synchronous machine inertia constant, the synchronous machine prime mover power and the synchronous machine inertia center time constant. The state variables of the synchronous machine rotor motion equation are the synchronous machine rotor position angle and the synchronous machine rotor angular velocity; the synchronous machine rotor motion equation is:

[0084] ;

[0085] Where:

[0086] ;

[0087] ;

[0088] In the formula, For the The synchronous machine rotor position angle, For the The synchronous machine rotor angular velocity, For the The inertia time constant of a synchronous machine, For the The power of the synchronous machine prime mover, For the Output power of synchronous machine, for The time constant of the center of inertia of a synchronous machine, for The inertia center power of synchronous machine, is the current synchronous machine number, is the total number of synchronous machines;

[0089] According to the synchronous machine rotor motion equation, the Lyapunov function of the synchronous machine based on the renewable energy power system is constructed;

[0090] According to the Lyapunov function, the stable domain boundary of the synchronous machine with respect to the state variable is obtained, and the stable domain boundary is the maximum level set of the Lyapunov function; the intersection of the Lyapunov function and the preset area D is obtained, thereby obtaining the stable domain boundary represented by the maximum level set of the Lyapunov function.

[0091] Based on the stability domain boundary, the transient stability of the new synchronous machine is judged according to the real-time numerical values ​​of the state variables after the fault. The transient stability of the synchronous machine is judged by observing whether the state variables of the new energy power system after the fault (synchronous machine rotor angular velocity and synchronous machine rotor position angle) are within the stability domain boundary, thereby conducting a safety and stability analysis of the new energy power system.

[0092] For a complex multi-machine power system with renewable energy access, the potential nodes in the synchronous machine and the renewable energy grid connection points in the system are retained, and the contraction admittance matrix of the renewable energy power system can be obtained as formula (3):

[0093] (3)

[0094] In the formula, Self-admittance for new energy grid connection points, , They are the mutual admittance between the potential nodes in the synchronous machine and the new energy grid connection point. is the self-admittance of the potential node in the synchronous machine, is the column vector composed of the transient potential of each synchronous machine, is the column vector composed of the voltages of each new energy grid connection point, The column vector composed of the current injected into each synchronous machine, A column vector consisting of the current injected into each renewable energy grid connection point;

[0095] From formula (3), the voltage of the new energy grid connection point can be solved by formula (4) and formula (5):

[0096] (4)

[0097] (5)

[0098] Consider the new energy grid connection point in the new energy power system to be equivalent to a new energy grid connection point, that is, Contains an element, expanding equation (5) into the amplitude and phase angle form gives equations (6) and (7):

[0099] (6)

[0100] (7)

[0101] In the formula, for The phase angle, is the synchronous machine rotor position angle, is the imaginary number symbol, It is the self-reactor of the new energy grid connection point. It is the mutual reactance between the synchronous machine and the new energy grid connection point;

[0102] Considering the new energy power system Synchronous machine and There are new energy grid-connected points, and the new energy grid-connected points only output active power, that is, and The phase of The voltage of the new energy grid connection point can be expressed as formula (8):

[0103] (8)

[0104] Further solving equation (8) yields equation (9):

[0105] (9)

[0106] From formula (9), the voltage expression of the new energy grid connection point is:

[0107] (10)

[0108] Solving equation (10), we get the voltage at the grid-connected point of renewable energy as equation (11):

[0109] (11)

[0110] In addition, the expression of the voltage phase angle of the new energy grid connection point is obtained from formula (9):

[0111] (12)

[0112] Solving equation (12), the voltage phase angle of the new energy grid connection point is:

[0113] (13)

[0114] In the formula, For the Voltage of each new energy grid connection point, For the A new energy grid-connected point self-reactor, is the synchronous machine serial number, is the total number of synchronous machines, For the The potential inside the synchronous machine, For the The first synchronous machine and the The reactance between the new energy grid connection points, For the The synchronous machine rotor position angle, For the The new energy grid-connected point injects current, For the The voltage phase angle of each new energy grid connection point.

[0115] In some preferred embodiments, see Figure 2 , the steps to construct the Lyapunov function are:

[0116] Based on the synchronous machine rotor motion equation, a sample set is obtained in a preset area, where the sample set is a set of numerical values ​​of state variables;

[0117] Initialize the parameters and number of iterations of the neural network;

[0118] Obtaining an output scalar function based on the sample set and the parameters of the neural network;

[0119] Obtaining an output risk function based on the sample set, the parameters of the neural network, the output scalar function and the equation of motion;

[0120] Input or set the operating parameters of the neural network, which include input dimension, output dimension, hidden layer dimension, learning rate and maximum number of iterations; obtain the input dimension according to the synchronous machine rotor motion equation, and obtain the output dimension according to the output scalar function. Preferably, a three-layer neural network with a preset hidden layer dimension of 7 and a learning rate of 0.01 is selected. During the operation, stochastic gradient descent is used as the optimizer;

[0121] Obtaining an activation function of the neural network, preferably, using the tanh function as the activation function, and in addition, the activation function is selected to be a function that can be derivated and whose function value includes both positive and negative values;

[0122] Running the neural network based on the running parameters, the parameters of the neural network, the number of iterations, the activation function, the output scalar function, and the output risk function to obtain an output function;

[0123] The Lyapunov function of the synchronous machine based on the renewable energy power system is obtained according to the output function.

[0124] In some of the preferred embodiments, see also Figure 2 , the operation steps of the neural network are:

[0125] Step 1: Judgement Is it established? In the formula, is the number of iterations, is the maximum number of iterations:

[0126] If not, modify the preset area or sample set;

[0127] If true, run the neural network;

[0128] Step 2: Update the parameters of the neural network according to the output risk function, and obtain the output function according to the output scalar function;

[0129] Step 3: Determine whether the output function meets the output verification conditions:

[0130] If the output function does not satisfy the output verification condition, then let , repeat steps 1 to 2;

[0131] If the output function satisfies the output verification condition, then the output function is a Lyapunov function.

[0132] The training process of a neural network is to update the parameters θ of the neural network to improve the output function to meet the output verification condition. On this basis, a loss function is established, which is defined as the output risk function. The output risk function is used to measure the degree to which the output function violates the output verification condition. Since the expected value of the parameters θ of the neural network must make the output function positive definite, the derivative of the output function negative definite, and V(0)=0, the output risk function is defined as:

[0133] ;

[0134] The first term corresponds to the positive definiteness of the output function, the second term corresponds to the negative definiteness of the derivative of the output function, and the third term represents the satisfaction of V(0) = 0. Since the desired output function is positive definite, negative values ​​of the output function must be penalized. Correspondingly, positive values ​​of the output function derivative should be penalized. In order to prevent the output function and the derivative of the output function from collapsing on zero, the margin is introduced and margins , where:

[0135] ,

[0136] ;

[0137] In the formula, is the output risk function, is the value of the state variable, are the parameters of the neural network, is the total number of samples, is the sample serial number, For the The value of the sample state variable, is the function corresponding to the synchronous machine rotor motion equation, For about The partial differential of represents transpose, for The constraint function is for The constraint function is is the output scalar function, is the margin distance of the output function from the origin, is the margin distance of the derivative of the output function from the origin, ≥0, ≥0, is the output function, is the derivative of the output function.

[0138] In some preferred embodiments, the step of determining whether the output function satisfies the output verification condition is:

[0139] Based on the solver, the verification function is obtained according to the sample set and the output function. The task of the verification function is to find the vector of state variables in the output function that violate the output verification condition. The verification function is the following first-order logic formula on real numbers;

[0140] ;

[0141] Where: To verify the function, is the total number of samples, is the sample serial number, For the The value of the sample state variable, To limit the small constant parameter that can tolerate numerical errors, is the value of the state variable, In the preset space There is a boundary in the middle, is the output function, is the derivative of the output function. In order to control the numerical sensitivity near the origin, , , is the set of positive rational numbers;

[0142] This effectively avoids pathological problems in numerical algorithms, such as arithmetic underflow. The values ​​inside this small ball correspond to physically insignificant perturbations. This is very important to eliminate the common numerical sensitivity problems in this algorithm. It should also be noted that The sphere does not affect the properties of the Lyapunov level set and its external attraction region.

[0143] Solvers are used to solve the verification function and determine whether the verification function holds; solving the verification function, i.e. solving these constraints, requires global minimization of highly non-convex functions (including the derivatives of the output function), which is a computationally complex and time-consuming task. It can rely on the results achieved in solving nonlinear constraints in Satisfiability Modulo Theories (SMT) solvers, such as dReal, which is prior art and has been used for similar design problems that do not involve neural networks.

[0144] Therefore, the SMT solver is used to verify whether the output function obtained in the previous step meets the output verification condition. If the output function does not meet the output verification condition, that is, the verification function does not hold, then the obtained counterexample is added to the sample set X to accelerate convergence. If the verification function holds, then the output function is the Lyapunov function that meets the output verification condition.

[0145] In some of the preferred embodiments, see also Figure 2 When the verification function is not established, the state variable value of the output function that does not meet the output verification condition is obtained according to the verification function, and the state variable value of the output function that does not meet the output verification condition is added to the sample set as a counterexample, and the sample set is updated to speed up the construction rate of the Lyapunov function; repeat steps 1 to 2 based on the updated sample set.

[0146] Furthermore, the output verification condition is:

[0147] ,

[0148] ;

[0149] In the formula, is the output function, is the value of the state variable, For the preset area, is the derivative of the output function.

[0150] Examples

[0151] In this example, the new energy power system is a three-machine nine-node system. Figure 3 , where G1 is the first synchronous machine, G2 is the second synchronous machine, G3 is the new energy station, and Bus-1 is the new energy grid connection point; retaining the potential nodes in the synchronous machine and the new energy grid connection point, the contraction admittance matrix of the new energy power system can be obtained as follows:

[0152]

[0153] The voltage at the new energy grid connection point It can be expressed as:

[0154]

[0155] Considering that the new energy grid-connected point only outputs active current, the phasor form is expanded to the following relationship:

[0156]

[0157] For the high-voltage transmission network, the line resistance is ignored, and since there is only one renewable energy station in this example, that is, only one renewable energy grid connection point, then , , we can get:

[0158]

[0159] Further written in the form of amplitude and phase angle, we have:

[0160]

[0161] The solution is: The voltage of the new energy grid connection point is:

[0162]

[0163] The voltage phase angle of the new energy grid connection point is:

[0164]

[0165] Substituting the voltage at the grid connection point of new energy and the voltage phase angle at the grid connection point of new energy into equation (1) to obtain the output power of the synchronous machine, and then substituting it into the synchronous machine rotor motion equation, the rotor motion equation of the synchronous machine G1 is obtained as follows:

[0166] ;

[0167] According to the rotor motion equation of synchronous machine G1, based on the new energy power system, the Lyapunov function of synchronous machine G1 is obtained by training the neural network under working condition 1. Working condition 1 is: =0, =42, =42, =3, , the Lyapunov function and its derivatives are as follows Figure 4 , Figure 5 As shown, Figure 4 is the Lyapunov function of synchronous machine G1 under working condition 1, Figure 5 The derivative of the Lyapunov function of the synchronous machine G1 under working condition 1;

[0168] The stable domain boundaries of the state variables synchronous machine rotor position angle and synchronous machine rotor angular velocity are obtained according to the Lyapunov function of the synchronous machine G1; based on the stable domain boundaries, the transient stability of the synchronous machine G1 is judged according to the real-time values ​​of the state variables after the fault.

[0169] According to the rotor motion equation of synchronous machine G1, based on the new energy power system, the Lyapunov function of synchronous machine G1 is obtained by training the neural network under working condition 2. Working condition 2 is: =0, =16, =25, =3, , the Lyapunov function and its derivatives are as follows Figure 6 , Figure 7 As shown, Figure 6 is the Lyapunov function of synchronous machine G1 under working condition 1, Figure 7 The derivative of the Lyapunov function of the synchronous machine G1 under working condition 2;

[0170] According to the Lyapunov function of synchronous machine G1, the stable domain boundaries of the state variables synchronous machine rotor position angle and synchronous machine rotor angular velocity are obtained, such as Figure 8 The blue line in the middle is the boundary of the stability region; based on the boundary of the stability region, the transient stability of the synchronous machine G1 is judged according to the real-time values ​​of the state variables after the fault.

[0171] Similarly, the rotor motion equation of synchronous machine G2 can be derived as follows:

[0172] ;

[0173] According to the rotor motion equation of the synchronous machine G2 and based on the new energy power system, a neural network is used to train the Lyapunov function of the synchronous machine G2 under preset working conditions. According to the Lyapunov function of the synchronous machine G2, the stable domain boundaries of the state variables of the synchronous machine rotor position angle and the synchronous machine rotor angular velocity are obtained; based on the stable domain boundaries, the transient stability of the synchronous machine G2 is judged according to the real-time numerical values ​​of the state variables after the fault.

[0174] The system embodiment described above is merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art may understand and implement it without creative work.

[0175] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0176] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A new energy power system security and stability analysis method based on Lyapunov function, characterized in that: The following steps are involved: Obtain the voltage at the grid connection point of the new energy power system, the voltage phase angle at the grid connection point of the new energy power system, the internal potential of the synchronous machine, the line susceptance and the rotor position angle of the synchronous machine; The output power of the synchronous machine is obtained according to the voltage at the new energy grid connection point, the voltage phase angle at the new energy grid connection point, the internal potential of the synchronous machine, the line susceptance and the synchronous machine rotor position angle; the output power of the synchronous machine is: ； In the formula, For the Output power of synchronous machine, For the The potential inside the synchronous machine, is the current synchronous machine number, is the synchronous machine serial number, is the total number of synchronous machines, For the The potential inside the synchronous machine, For the The first synchronous machine and the The line susceptance between the synchronous machines, For the The synchronous machine rotor position angle, For the The synchronous machine rotor position angle, It is the serial number of the new energy grid connection point. is the total number of new energy grid-connected points, For the Voltage of each new energy grid connection point, For the The first synchronous machine and the The line impedance between the new energy grid connection points is For the Voltage phase angle of each new energy grid connection point; Based on the new energy power system, obtaining the synchronous machine inertia constant, the synchronous machine prime mover power and the synchronous machine inertia center time constant; Obtaining a synchronous machine rotor motion equation according to the synchronous machine inertia constant, the synchronous machine prime mover power, the synchronous machine inertia center time constant and the synchronous machine output power, wherein the state variables of the synchronous machine rotor motion equation are the synchronous machine rotor position angle and the synchronous machine rotor angular velocity; Constructing a Lyapunov function of a synchronous machine based on the new energy power system according to the synchronous machine rotor motion equation; Obtaining the stability domain boundary of the synchronous machine with respect to the state variable according to the Lyapunov function; Based on the stability region boundary, judging the transient stability of the synchronous machine according to the real-time value of the state variable after the fault; The steps of constructing the Lyapunov function are: Based on the synchronous machine rotor motion equation, a sample set is acquired in a preset area, wherein the sample set is a set of values ​​of the state variables; Initialize the parameters and number of iterations of the neural network; Obtaining an output scalar function based on the sample set and the parameters of the neural network; Obtaining an output risk function according to the sample set, the parameters of the neural network, the output scalar function and the equation of motion; Inputting or setting the operating parameters of the neural network, the operating parameters including input dimension, output dimension, hidden layer dimension, learning rate and maximum number of iterations; obtaining the input dimension according to the synchronous machine rotor motion equation, and obtaining the output dimension according to the output scalar function; Obtaining an activation function of the neural network; Running the neural network based on the operating parameters, the parameters of the neural network, the number of iterations, the activation function, the output scalar function, and the output risk function to obtain an output function; A Lyapunov function of a synchronous machine based on the new energy power system is obtained according to the output function.

2. The method for safety and stability analysis of new energy power systems based on Lyapunov function according to claim 1 is characterized in that: The voltage of the new energy grid connection point is: ； The voltage phase angle of the new energy grid connection point is: In the formula, For the Voltage of each new energy grid connection point, For the A new energy grid-connected point self-reactor, is the synchronous machine serial number, is the total number of synchronous machines, For the The potential inside the synchronous machine, For the The first synchronous machine and the The reactance between the new energy grid connection points, For the The synchronous machine rotor position angle, For the The new energy grid-connected point injects current, For the The voltage phase angle of each new energy grid connection point.

3. The method for safety and stability analysis of new energy power systems based on Lyapunov function according to claim 1 or 2, characterized in that: The synchronous machine rotor motion equation is: ； Where: ； ； In the formula, For the The synchronous machine rotor position angle, For the The synchronous machine rotor angular velocity, For the The inertia time constant of a synchronous machine, For the The power of the synchronous machine prime mover, For the Output power of synchronous machine, for The time constant of the center of inertia of a synchronous machine, for The inertia center power of synchronous machine, is the current synchronous machine number, is the total number of synchronous machines.

4. The method for safety and stability analysis of new energy power systems based on Lyapunov function according to claim 1 is characterized in that: The operation steps of the neural network are: Step 1: Judgement Is it established? In the formula, is the number of iterations, is the maximum number of iterations: If not, modify the preset area or the sample set; If established, the neural network is run; Step 2: updating the parameters of the neural network according to the output risk function, and obtaining the output function according to the output scalar function; Step 3: Determine whether the output function meets the output verification condition: If the output function does not satisfy the output verification condition, then , repeat step 1 to step 2; If the output function satisfies the output verification condition, then the output function is the Lyapunov function.

5. The method for safety and stability analysis of new energy power systems based on Lyapunov function according to claim 4 is characterized in that: The output risk function is: ； Where: ， ； In the formula, is the output risk function, is the value of the state variable, are the parameters of the neural network, is the total number of samples, is the sample serial number, For the The value of the sample state variable, is the function corresponding to the synchronous machine rotor motion equation, About The partial differential of represents transpose, for The constraint function is for The constraint function is is the output scalar function, is the margin distance of the output function from the origin, is the margin distance of the derivative of the output function from the origin, ≥0, ≥0, is the output function, is the derivative of the output function.

6. The method for security and stability analysis of new energy power systems based on Lyapunov function according to claim 4 is characterized in that: The steps of judging whether the output function satisfies the output verification condition are: Based on the solver, a verification function is obtained according to the sample set and the output function, wherein the verification function is: ； Where: To verify the function, is the total number of samples, is the sample serial number, For the The value of the sample state variable, To limit the small constant parameter that can tolerate numerical errors, is the value of the state variable, is the output function, is the derivative of the output function, , is the set of positive rational numbers; Using the solver to solve the verification function and determine whether the verification function is established; If the verification function does not hold, then the output function does not satisfy the output verification condition; If the verification function holds, the output function satisfies the output verification condition.

7. The method for safety and stability analysis of new energy power systems based on Lyapunov function according to claim 6 is characterized in that: When the verification function does not hold, obtain the state variable value of the output function that does not satisfy the output verification condition according to the verification function, add the state variable value of the output function that does not satisfy the output verification condition to the sample set, and update the sample set; repeat steps 1 to 2 based on the updated sample set.

8. The method for analyzing the safety and stability of a new energy power system based on Lyapunov function according to any one of claims 4 to 7, characterized in that: The output verification conditions are: ， ； In the formula, is the output function, is the value of the state variable, For the preset area, is the derivative of the output function.

9. The method for security and stability analysis of new energy power systems based on Lyapunov function according to claim 1 is characterized in that: The hidden layer dimension is 7.

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