Method for analyzing safety and stability of new-energy power system on basis of lyapunov function

Abstract

Disclosed in the present disclosure is a method for analyzing the safety and stability of a new-energy power system on the basis of a Lyapunov function. The method comprises the following steps: acquiring the voltage of a new-energy grid connection point, the voltage phase angle of the new-energy grid connection point, the internal electromotive force of a synchronous machine, a line susceptance, and the rotor position angle of the synchronous machine in a new-energy power system, so as to obtain the output power of the synchronous machine; on the basis of the new-energy power system and the output power of the synchronous machine, obtaining a rotor motion equation of the synchronous machine; on the basis of the rotor motion equation of the synchronous machine, constructing a Lyapunov function based on the synchronous machine in the new-energy power system; on the basis of the Lyapunov function, obtaining a stability region boundary of the synchronous machine with respect to state variables; and on the basis of the stability region boundary and real-time values of post‑fault state variables, determining the transient stability of the synchronous machine. The method for analyzing the safety and stability of a new-energy power system on the basis of a Lyapunov function provided in the present disclosure features low construction difficulty, is universally applicable to nonlinear systems of different forms, and enables fast and accurate transient stability assessment.

Description

New energy power system security and stability analysis method based on Lyapunov function

[0001] The present application claims priority to the Chinese patent application No. 202411097144.3 filed on August 12, 2024 with the Chinese Patent Office, the content of which is incorporated herein by reference in its entirety. TECHNICAL FIELD

[0002] The present disclosure relates to the technical field of new energy station safety analysis, in particular to a new energy power system security and stability analysis method based on Lyapunov function. BACKGROUND

[0003] Since the goal of "carbon peak and carbon neutrality" was proposed, the construction of new-type power system dominated by clean energy has become the main development direction of China's future energy power, and high proportion of new energy access will become the basic characteristics and development form of modern power system. However, the increasing load demand, the operation condition closer to the system limit, the larger interconnected power grid and more new energy units connected through power electronic components make the modern power system more complex, and the power system operation faces more severe challenges. In order to provide safe and reliable power service, the stability of these modern power systems and power supply equipment must be maintained. The growth and evolution of modern power system scale and the operation condition close to the limit of power system lead to different forms of instability problems. Therefore, the stability of modern power system becomes more and more important for the safe operation of power grid. SUMMARY

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

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

[0006] Obtaining the new energy grid-connected point voltage, the new energy grid-connected point voltage phase angle, the synchronous machine internal potential, the line admittance and the synchronous machine rotor position angle of the new energy power system;

[0007] Obtaining the synchronous machine output power according to the new energy grid-connected point voltage, the new energy grid-connected point voltage phase angle, the synchronous machine internal potential, the line admittance and the synchronous machine rotor position angle; the synchronous machine output power is:

[0008] In the formula, P gk is the output power of the kth synchronous machine, Egk is the internal voltage of the kth synchronous machine, k is the current synchronous machine number, m is the synchronous machine number, n is the total number of synchronous machines, E gm is the internal voltage of the mth synchronous machine, B mk is the line susceptance between the kth synchronous machine and the mth synchronous machine, δ gk is the rotor position angle of the kth synchronous machine, δ gm is the rotor position angle of the mth synchronous machine, i is the new energy grid point number, l is the total number of new energy grid points, U bi is the voltage of the i th new energy grid point, B wgik is the line susceptance between the kth synchronous machine and the i th new energy grid point, δ bi is the voltage phase angle of the i th new energy grid point.

[0009] Based on the new energy power system, the inertia constant of the synchronous machine, the prime mover power of the synchronous machine and the inertia center time constant of the synchronous machine are obtained;

[0010] According to the inertia constant of the synchronous machine, the prime mover power of the synchronous machine, the inertia center time constant of the synchronous machine and the output power of the synchronous machine, the rotor motion equation of the synchronous machine is obtained, and the state variable of the rotor motion equation of the synchronous machine is the rotor position angle and the rotor angular velocity of the synchronous machine;

[0011] According to the rotor motion equation of the synchronous machine, the Lyapunov function of the synchronous machine based on the new energy power system is constructed;

[0012] According to the Lyapunov function, the stability domain boundary of the synchronous machine with respect to the state variable is obtained;

[0013] Based on the stability domain boundary, the transient stability of the synchronous machine is judged according to the real-time value of the state variable after the fault. Further, the new energy grid point voltage is:

[0014] The voltage phase angle of the new energy grid point is:

[0015] In the formula, U bi is the voltage of the i th new energy grid point, X wwi is the self-reactance of the i th new energy grid point, m is the synchronous machine number, n is the total number of synchronous machines, E gm is the internal voltage of the mth synchronous machine, X wgim is the reactance between the mth synchronous machine and the i th new energy grid point, δ gm is the rotor position angle of the mth synchronous machine, I wi is the injection current of the i th new energy grid point, δ bi is the voltage phase angle of the i th new energy grid point.

[0016] Further, the synchronous machine rotor motion equation is:

[0017] In the formula, δ

[0018] In the formula, δ gk is the rotor position angle of the kth synchronous machine, ω k is the rotor angular velocity of the kth synchronous machine, M k is the inertia time constant of the kth synchronous machine, P k is the prime mover power of the kth synchronous machine, P gk is the output power of the kth synchronous machine, M COI is the inertia center time constant of the n synchronous machines, P COI is the inertia center power of the n synchronous machines, k is the current synchronous machine serial number, and n is the total number of synchronous machines.

[0019] Further, the step of constructing the Lyapunov function is:

[0020] Based on the synchronous machine rotor motion equation, a sample set is obtained in a preset region, and the sample set is a set of numerical values of the state variables;

[0021] The parameters of the neural network and the number of iterations are initialized;

[0022] Based on the sample set and the parameters of the neural network, an output scalar function is obtained;

[0023] According to the sample set, the parameters of the neural network, the output scalar function and the motion equation, an output risk function is obtained;

[0024] The running parameters of the neural network are input or set, the running parameters include input dimension, output dimension, hidden layer dimension, learning rate and maximum iteration number; the input dimension is obtained according to the synchronous machine rotor motion equation, and the output dimension is obtained according to the output scalar function;

[0025] The activation function of the neural network is obtained;

[0026] 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, the neural network is run to obtain an output function;

[0027] According to the output function, the Lyapunov function of the synchronous machine based on the new energy power system is obtained.

[0028] Further, the running step of the neural network is:

[0029] Step 1: judge t<tmax is true, wherein t is the iteration number, t max is the maximum iteration number:

[0030] is not true, the preset region or the sample set is modified;

[0031] is true, the neural network is run;

[0032] 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;

[0033] Step 3: judging whether the output function satisfies an output verification condition:

[0034] If the output function does not satisfy the output verification condition, t is set to t+1, and the steps 1 to 2 are repeated.

[0035] If the output function satisfies the output verification condition, the output function is the Lyapunov function.

[0036] Further, the output risk function is:

[0037] wherein:

[0038] wherein L is the output risk function, x is the numerical value of the state variable, θ is the parameter of the neural network, N is the total number of samples, s is the sample serial number, x s is the numerical value of the s-th sample state variable, f is a function corresponding to the synchronous machine rotor motion equation, is the partial differential with respect to x, T represents transposition, h1 is the constraint function of V, h2 is the constraint function of is the output scalar function, m1 is the edge distance of the output function from the origin, m2 is the edge distance of the derivative of the output function from the origin, m1≥0, m2≥0, V is the output function, is the derivative of the output function.

[0039] Further, the step of judging whether the output function satisfies the output verification condition is:

[0040] Based on the solver, a verification function is obtained according to the sample set and the output function, and the verification function is:

[0041] wherein: Ф is the verification function, N is the total number of samples, s is the sample serial number, x s is the numerical value of the s-th sample state variable, ε is a small constant parameter limiting the tolerable numerical error, x is the numerical value of the state variable, and V is the output function, ε∈Q + Q + is a set of positive rational numbers;

[0042] solving the verification function by using the solver, and determining whether the verification function is established or not;

[0043] if the verification function is not established, the output function does not satisfy the output verification condition;

[0044] if the verification function is established, the output function satisfies the output verification condition.

[0045] Further, when the verification function is not established, a state variable value of the output function which does not satisfy the output verification condition is obtained according to the verification function, the state variable value of the output function which does not satisfy the output verification condition is added to the sample set, and the sample set is updated; the steps 1 to 2 are repeated based on the updated sample set.

[0046] Further, the output verification condition is: V(0)=0 and V(x)>0 in D-{0},

[0047] wherein, V is an output function, x is a value of a state variable, D is a preset region, is a derivative of the output function.

[0048] Further, the dimension of the hidden layer is 7. BRIEF DESCRIPTION OF DRAWINGS

[0049] Fig. 1 is a schematic diagram of steps of an analysis method of the present disclosure;

[0050] Fig. 2 is a schematic diagram of a process of constructing a Lyapunov function in the present disclosure;

[0051] Fig. 3 is a schematic diagram of a topological network structure of a three-machine nine-node new energy power system in an example of the present disclosure;

[0052] Fig. 4 is a Lyapunov function of a synchronous machine G1 under a working condition 1 in an example of the present disclosure;

[0053] Fig. 5 is a derivative of the Lyapunov function of the synchronous machine G1 under the working condition 1 in the example of the present disclosure;

[0054] Fig. 6 is a Lyapunov function of a synchronous machine G1 under a working condition 2 in an example of the present disclosure;

[0055] Fig. 7 is a derivative of the Lyapunov function of the synchronous machine G1 under the working condition 2 in the example of the present disclosure;

[0056] Fig. 8 is a schematic diagram of the stability region boundary under working condition 2 in the example of the present disclosure. DETAILED DESCRIPTION

[0057] Online transient stability assessment is conducive to timely measures to maintain power system stability, and is of great significance for the prospective scheduling and planning of the power system. With the wide deployment of phasor measurement units in the power grid, a large amount of 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 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 of the power system under study and the stability state can be fully revealed. As a data-driven stability discrimination, these relationships can be used to achieve fast and accurate transient stability assessment.

[0058] 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 transition to a new state or return to the original stable operating state after the power system is subjected to a large disturbance. Transient instability is also a major factor leading to large-area power system blackouts, which can 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, mainly using energy functions and sum-of-squares programming methods. The sum-of-squares programming method is limited to polynomial systems, and for non-polynomial systems, the motion equation needs to be approximated using Taylor expansion, and then the stability domain is calculated based on the approximated polynomial equation. 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 cannot be integrated and cannot obtain energy functions, and cannot handle different forms of nonlinear systems. There is no general Lyapunov function construction method for power systems with new energy access.

[0059] The beneficial effects of the present disclosure are:

[0060] 1. The present disclosure calculates the synchronous generator output power according to the new energy grid point voltage, the new energy grid point voltage phase angle, the synchronous machine internal potential, the line admittance and the synchronous machine rotor position angle in the new energy power system, and obtains the synchronous machine rotor motion equation based on the synchronous generator output power to construct the Lyapunov function, linearizes the complex nonlinear system, reduces the construction difficulty of the Lyapunov function, and provides a general construction method for the Lyapunov function of different forms of power systems with new energy access;

[0061] 2. The stable domain boundary determined based on the Lyapunov function constructed according to the present application, the transient stability of the synchronous machine is judged by observing the real-time values of the position angle and the angular velocity of the rotor of the synchronous machine in the new energy power system after the fault, and judging whether the two state variables are located within the stable domain boundary, and then the safety and stability of the new energy power system is analyzed, and the fast and accurate transient stability evaluation of the new energy power system is realized.

[0062] The construction of the Lyapunov function of the synchronous machine in the new energy power system is restricted in the prior art. In order to maintain the safe and stable operation of the power supply system and prevent the occurrence of large-area power failure events, a rapid and accurate transient stability evaluation method is urgently needed, which is suitable for safety and stability analysis of the power system with new energy access, and provides information support for the prevention and effective development of emergency control measures for the transient stable operation of the new energy power system after the fault.

[0063] In order to clearly illustrate the technical features of the present application, the present application will be described in detail below through specific embodiments.

[0064] The embodiment of the present application provides a safety and stability analysis method of a new energy power system based on a Lyapunov function, specifically, the new energy power system has n synchronous machines and l new energy grid points, and the output power of the kth synchronous machine is formula (1):

[0065] In the formula, P gk is the output power of the kth synchronous machine, Re represents the real part, is the derivative of the internal potential of the kth synchronous machine, k is the current synchronous machine number, m is the synchronous machine number, n is the total number of synchronous machines, is the conjugate of the injected current of the kth synchronous machine, is the conjugate of the admittance between the kth synchronous machine and the mth synchronous machine, is the phasor of the derivative of the internal potential of the mth synchronous machine, i is the new energy grid point number, and l is the total number of new energy grid points, is the conjugate of the mutual admittance between the kth synchronous machine and the i th new energy grid point, is the phasor of the derivative of the voltage of the i th new energy grid point;

[0066] When the line resistance is ignored, formula (1) can be expressed as formula (2):

[0067] In the formula, P gk is the output power of the kth synchronous machine, E gk is the internal potential of the kth synchronous machine, k is the current synchronous machine number, m is the synchronous machine number, n is the total number of synchronous machines, E gm is the internal potential of the mth synchronous machine, and Bmk is the line reactance between the kth synchronous machine and the mth synchronous machine, δ gk is the rotor position angle of the kth synchronous machine, δ gm is the rotor position angle of the mth synchronous machine, i is the serial number of the new energy grid-connected point, and l is the total number of new energy grid-connected points, U bi is the voltage of the i th new energy grid-connected point, B wgik is the line reactance between the kth synchronous machine and the i th new energy grid-connected point, δ bi is the phase angle of the voltage of the i th new energy grid-connected point;

[0068] Therefore, based on formula (2), after obtaining the new energy grid-connected point voltage, the new energy grid-connected point voltage phase angle, the synchronous machine internal potential, the line reactance, and the synchronous machine rotor position angle of the new energy power system, the synchronous machine output power can be calculated according to formula (1); the complex nonlinear system is linearized and converted, and the construction difficulty of the Lyapunov function suitable for the new energy power system is reduced;

[0069] Based on formula (2), based on the new energy power system, the synchronous machine inertia constant, the synchronous machine prime mover power, and the synchronous machine inertia center time constant can be obtained, and the synchronous machine rotor motion equation can be obtained, 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:

[0070] In the formula:

[0071] In the formula, δ gk is the rotor position angle of the kth synchronous machine, ω k is the rotor angular velocity of the kth synchronous machine, M k is the inertia time constant of the kth synchronous machine, P k is the prime mover power of the kth synchronous machine, P gk is the output power of the kth synchronous machine, M COI is the inertia center time constant of the n synchronous machines, P COI is the inertia center power of the n synchronous machines, k is the current synchronous machine serial number, and n is the total number of synchronous machines;

[0072] According to the synchronous machine rotor motion equation, the Lyapunov function of the synchronous machine based on the new energy power system is constructed;

[0073] According to the Lyapunov function, the stable domain boundary of the synchronous machine with respect to the state variable is obtained, the stable domain boundary is the maximum level set of the Lyapunov function; the intersection of the Lyapunov function and the preset region D is obtained, and thus the stable domain boundary represented by the maximum level set of the Lyapunov function is obtained.

[0074] Based on the stable domain boundary, the transient stability of the new synchronous machine is judged according to the real-time numerical value of the state variable after the fault, and the transient stability of the synchronous machine is judged by observing whether the state variable (rotor angle speed and rotor position angle of the synchronous machine) of the new energy power system after the fault is located in the stable domain boundary, so as to analyze the safety and stability of the new energy power system.

[0075] For a complex multi-machine power system with new energy access, the potential node in the synchronous machine and the new energy grid connection point in the system are retained, and the reduced admittance matrix of the new energy power system is obtained as formula (3):

[0076] In the formula, Y ww is the self-admittance of the new energy grid connection point, Y gw and Y wg are mutual admittances between the potential node in the synchronous machine and the new energy grid connection point, Y gg is the self-admittance of the potential node in the synchronous machine, E g is a column vector composed of transient potentials of each synchronous machine, U b is a column vector composed of voltages of each new energy grid connection point, I g is a column vector composed of injection currents of each synchronous machine, and I w is a column vector composed of injection currents of each new energy grid connection point.

[0077] The voltage of the new energy grid connection point can be solved by formula (4) and formula (5) according to formula (3): I w -Y ww U b =Y wg E g (5)

[0078] Considering that the new energy grid connection point in the new energy power system is equivalent to one new energy grid connection point, Y ww contains one element, and formula (5) is expanded into amplitude and phase angle form, then formula (6) and formula (7) are obtained: I w ∠δ w -Y ww U b ∠δ w =Y wg E g ∠δ g (6)

[0079] In the formula, δ w is the phase angle of I w , δ g is the rotor position angle of the synchronous machine, j is the imaginary symbol, and X wwX wg is the mutual reactance between the i-th new energy grid point and the m-th synchronous machine.

[0080] Considering that there are n synchronous machines and l new energy grid points in the new energy power system, and the new energy grid points only output active power, i.e. w U b is the phase of the i-th new energy grid point voltage, then the i-th new energy grid point voltage can be expressed as formula (8):

[0081] Further solving formula (8) can obtain formula (9):

[0082] The expression of the new energy grid point voltage obtained from formula (9) is:

[0083] Solving formula (10) obtains the new energy grid point voltage as formula (11):

[0084] In addition, the expression of the new energy grid point voltage phase angle obtained from formula (9) is:

[0085] Solving formula (12) obtains the new energy grid point voltage phase angle:

[0086] In the formula, U bi is the i-th new energy grid point voltage, X wwi is the i-th new energy grid point self-reactance, m is the synchronous machine number, n is the total number of synchronous machines, E gm is the internal potential of the m-th synchronous machine, X wgim is the reactance between the m-th synchronous machine and the i-th new energy grid point, δ gm is the rotor position angle of the m-th synchronous machine, I wi is the i-th new energy grid point injection current, δ bi is the i-th new energy grid point voltage phase angle.

[0087] In some preferred embodiments, referring to FIG. 2, the step of constructing the Lyapunov function is:

[0088] Based on the synchronous machine rotor motion equation, a sample set is obtained in a preset region, and the sample set is a collection of numerical values of state variables;

[0089] Initializing the parameters of the neural network and the number of iterations;

[0090] Obtaining the output scalar function based on the sample set and the parameters of the neural network;

[0091] An output risk function is obtained according to the sample set, the parameter of the neural network, the output scalar function and the motion equation;

[0092] An operation parameter of the neural network is inputted or set, and the operation parameter includes an input dimension, an output dimension, a hidden layer dimension, a learning rate and a maximum iteration number; the input dimension is obtained according to the motion equation of the rotor of the synchronous machine, and the output dimension is obtained according to the output scalar function; preferably, a three-layer neural network with a preset hidden layer dimension of 7 is selected, the learning rate is 0.01, and a stochastic gradient descent is used as an optimizer in the running process;

[0093] An activation function of the neural network is obtained, and preferably, a tanh function is used as the activation function; in addition, the selection condition of the activation function is that the function is derivable and the function value includes both positive and negative values;

[0094] The neural network is run based on the operation parameter, the parameter of the neural network, the iteration number, the activation function, the output scalar function and the output risk function, and an output function is obtained;

[0095] A Lyapunov function of the synchronous machine based on the new energy power system is obtained according to the output function.

[0096] In some preferred embodiments, referring also to FIG. 2, the running steps of the neural network are as follows:

[0097] Step 1: it is judged whether t < t max is established, wherein t is an iteration number, and t max is a maximum iteration number:

[0098] If not, the preset region or the sample set is modified;

[0099] If yes, the neural network is run;

[0100] Step 2: the parameter of the neural network is updated according to the output risk function, and an output function is obtained according to the output scalar function;

[0101] Step 3: it is judged whether the output function meets an output verification condition:

[0102] If the output function does not meet the output verification condition, t is set to t+1, and steps 1 to 2 are repeated;

[0103] If the output function meets the output verification condition, the output function is a Lyapunov function.

[0104] The training process of the neural network is to update the parameters θ of the neural network to improve the output function to satisfy the output verification condition, on the basis of which a loss function is established, which is defined as an output risk function. The output risk function is used to measure the degree of violation of the output function against 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(θ) = 0, the output risk function is defined as:

[0105] 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 degree of satisfaction of V(θ) = 0. Since the desired output function is positive definite, the negative value of the output function must be punished. Correspondingly, the derivative of the output function with positive value should be punished. In order to avoid the output function and the derivative of the output function collapsing on zero, the margin m1 and the margin m2 are introduced, where:

[0106] In the formula, L is the output risk function, x is the value of the state variable, θ is the parameter of the neural network, N is the total number of samples, s is the sample serial number, x s is the value of the state variable of the s-th sample, f is the function corresponding to the synchronous machine rotor motion equation, is the partial derivative with respect to x, T represents transposition, h1 is the constraint function of V, h2 is the constraint function of is the output scalar function, m1 is the margin of the output function from the origin, m2 is the margin of the derivative of the output function from the origin, m1 ≥ 0, m2 ≥ 0, V is the output function, is the derivative of the output function.

[0107] In some preferred embodiments, the step of judging whether the output function satisfies the output verification condition is:

[0108] Based on the solver, the verification function is obtained according to the sample set and the output function, and the task of the verification function is to find the vector of the state variable that violates the output verification condition in the output function. The verification function is a first-order logic formula on the following real numbers:

[0109] In the formula: Ф is the verification function, N is the total number of samples, s is the sample serial number, x s is the value of the state variable of the s-th sample, ε is a small constant parameter limiting the tolerable numerical error, x is the value of the state variable, x is bounded in the preset space D, V is the output function, is the derivative of the output function, in order to control the numerical sensitivity near the origin, ε is introduced, ε ∈ Q + , Q + is a set of positive rational numbers;

[0110] ε effectively avoids ill-conditioned problems in numerical algorithms, such as arithmetic underflow. The values inside the ε-ball correspond to physically unimportant perturbations. The ε is important to eliminate numerical sensitivity problems that are common in this algorithm. It should also be noted that the ε-ball does not affect the properties of the Lyapunov level sets and their outer attracting regions.

[0111] The solver is used to solve the verification function and determine whether the verification function is valid; solving the verification function means that the global minimization of the highly non-convex function (including the derivative of the output function) is required, which is a relatively complex and time-consuming task. It can rely on the achievements made in solving nonlinear constraints in Satisfiability Modulo Theories (SMT) solvers, such as dReal, which is a prior art and has been used in similar design problems that do not involve neural networks.

[0112] Therefore, the SMT solver is used to verify whether the output function obtained in the previous step satisfies the output verification condition. If the output function does not satisfy the output verification condition, i.e., the verification function is not valid, the counterexample obtained is added to the sample set X to accelerate convergence, and if the verification function is valid, the output function is the Lyapunov function that satisfies the output verification condition.

[0113] In some preferred embodiments, referring also to FIG. 2, when the verification function is not valid, the state variable values for which the output function does not satisfy the output verification condition are obtained according to the verification function, the state variable values for which the output function does not satisfy the output verification condition are added to the sample set as counterexamples, and the sample set is updated to accelerate the construction rate of the Lyapunov function; the updated sample set is used as the basis for repeating steps 1 to 2.

[0114] Further, the output verification condition is: V(0) = 0 and V(x) > 0 in D-{0},

[0115] In the formula, V is the output function, x is the value of the state variable, D is a predetermined region, is the derivative of the output function.

[0116] Examples

[0117] In this example, the new energy power system is a three-machine nine-node system, as shown in FIG. 3, wherein 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; the potential nodes inside the synchronous machine and the new energy grid connection point are retained, and the reduced admittance matrix of the new energy power system is:

[0118] The voltage U of the new energy grid connection point b can be expressed as:

[0119] Considering that the new energy grid-connected point only outputs active current, the phasor form is expanded as follows:

[0120] For a high-voltage transmission network, the line resistance is ignored, and since there is only one new energy station in this example, i.e., only one new energy grid-connected point, U bi = U b1 = U b , δ bi = δ b1 = δ b , and the following can be obtained:

[0121] Further written in the form of amplitude and phase angle, the following is obtained:

[0122] The solution is that the new energy grid-connected point voltage is:

[0123] and the phase angle of the new energy grid-connected point voltage is:

[0124] Substitute the new energy grid-connected point voltage and the phase angle of the new energy grid-connected point voltage into equation (1) to obtain the synchronous machine output power, and then substitute it into the synchronous machine rotor motion equation to obtain the rotor motion equation of the synchronous machine G1:

[0125] According to the rotor motion equation of the synchronous machine G1, based on the new energy power system, the Lyapunov function of the synchronous machine G1 is obtained by training using a neural network under working condition 1, and the working condition 1 is: δ g2 = 0, T J1 = 42, D = 42, I wi = I w1 = I w = 3, M1 = T J1 / 314, and the Lyapunov function and its derivative are shown in FIG. 4 and FIG. 5, wherein FIG. 4 is the Lyapunov function of the synchronous machine G1 under working condition 1, and FIG. 5 is the derivative of the Lyapunov function of the synchronous machine G1 under working condition 1.

[0126] According to the Lyapunov function of the synchronous machine G1, the stability domain boundary of the state variables, i.e., the synchronous machine rotor position angle and the synchronous machine rotor angular velocity, is obtained; based on the stability domain boundary, the transient stability of the synchronous machine G1 is judged according to the real-time numerical value of the state variables after the fault.

[0127] According to the rotor motion equation of the synchronous machine G1, based on the new energy power system, the Lyapunov function of the synchronous machine G1 is obtained by training using a neural network under working condition 2, and the working condition 2 is: δ g2 = 0, TJ1 = 16, D = 25, I wi = I w1 = I w = 3, M2 = T J1 / 314, the Lyapunov function and its derivative are shown in FIG. 6 and FIG. 7, FIG. 6 is a Lyapunov function of the synchronous machine G1 under working condition 1, and FIG. 7 is a derivative of the Lyapunov function of the synchronous machine G1 under working condition 2;

[0128] According to the Lyapunov function of the synchronous machine G1, the stability domain boundary of the state variable synchronous machine rotor position angle and the synchronous machine rotor angular velocity is obtained, and the stability domain boundary is shown as a blue line in FIG. 8; based on the stability domain boundary, the transient stability of the synchronous machine G1 is judged according to the real-time value of the state variable after the fault.

[0129] Similarly, the rotor motion equation of the synchronous machine G2 can be derived as:

[0130] According to the rotor motion equation of the synchronous machine G2, the Lyapunov function of the synchronous machine G2 is obtained based on the new energy power system and by using a neural network under a preset working condition; according to the Lyapunov function of the synchronous machine G2, the stability domain boundary of the state variable synchronous machine rotor position angle and the synchronous machine rotor angular velocity is obtained; based on the stability domain boundary, the transient stability of the synchronous machine G2 is judged according to the real-time value of the state variable after the fault.

[0131] The system embodiments described above are only schematic, wherein the units shown as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e., can be located in one place or distributed on a plurality of network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the embodiments. Those skilled in the art can understand and implement without creative labor.

[0132] From the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software plus necessary general hardware platforms, and of course can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of software products, which can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and include a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0133] The above merely describes the preferred embodiments of the present disclosure, and it should be pointed out that, for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present disclosure, and these improvements and modifications should also be considered as the protection scope of the present disclosure.

Claims

1. A Lyapunov function based security and stability analysis method for new energy power systems, characterized in that, The method comprises the following steps: acquiring a new energy grid-connected point voltage, a new energy grid-connected point phase angle, an internal potential of a synchronous machine, a line admittance, and a rotor position angle of the synchronous machine of a new energy power system; The synchronous machine output power is obtained according to the new energy grid-connected point voltage, the new energy grid-connected point voltage phase angle, the synchronous machine internal potential, the line electric susceptance and the synchronous machine rotor position angle; the synchronous machine output power is: In the formula, P gk is the output power of the kth synchronous machine, E gk is the internal potential of the kth synchronous machine, k is the current synchronous machine sequence number, m is the synchronous machine sequence number, n is the total number of synchronous machines, E gm is the internal potential of the mth synchronous machine, B mk is the line admittance between the kth synchronous machine and the mth synchronous machine, δ gk is the rotor position angle of the kth synchronous machine, δ gm is the rotor position angle of the mth synchronous machine, i is the new energy grid connection point sequence number, l is the total number of new energy grid connection points, U bi is the voltage of the i th new energy grid connection point, B wgik is the line admittance between the kth synchronous machine and the i th new energy grid connection point, δ bi is the voltage phase angle of the i th new energy grid connection point; based on the new energy power system, acquiring an inertia constant of the synchronous machine, a prime mover power of the synchronous machine, and an inertia center time constant of the synchronous machine; obtaining a rotor motion equation of the synchronous machine according to the inertia constant of the synchronous machine, the prime mover power of the synchronous machine, the inertia center time constant of the synchronous machine, and an output power of the synchronous machine, wherein a state variable of the rotor motion equation of the synchronous machine is the rotor position angle of the synchronous machine and a rotor angular velocity of the synchronous machine; constructing a Lyapunov function of the synchronous machine based on the new energy power system according to the rotor motion equation of the synchronous machine; obtaining a stability domain boundary of the synchronous machine with respect to the state variable according to the Lyapunov function; judging the transient stability of the synchronous machine according to real-time values of the state variable based on the stability domain boundary.

2. The Lyapunov function based security stability analysis method of new energy power system according to claim 1, characterized in that, The new energy grid-connected point voltage is: The new energy grid-connected point voltage phase angle is: In the formula, U bi is the voltage of the i-th new energy grid-connected point, X wwi is the self-reactance of the i-th new energy grid-connected point, m is the serial number of the synchronous machine, n is the total number of the synchronous machines, E gm is the internal potential of the m-th synchronous machine, X wgim is the reactance between the m-th synchronous machine and the i-th new energy grid-connected point, δ gm is the rotor position angle of the m-th synchronous machine, I wi is the injected current of the i-th new energy grid-connected point, δ bi is the phase angle of the voltage of the i-th new energy grid-connected point.

3. The Lyapunov function based security stability analysis method of new energy power system according to claim 1 or 2, characterized in that, The synchronous machine rotor motion equation is: In the formulae: where δ gk is the kth synchronous machine rotor position angle, ω k is the kth synchronous machine rotor angular velocity, M k is the kth synchronous machine inertia time constant, P k is the kth synchronous machine prime mover power, P gk is the kth synchronous machine output power, M COI is the n synchronous machine inertia center time constant, P COI is the n synchronous machine inertia center power, k is the current synchronous machine sequence number, and n is the total number of synchronous machines.

4. The Lyapunov function based security stability analysis method of new energy power system according to any one of claims 1-3, characterized in that, The step of constructing the Lyapunov function comprises the following steps: acquiring a sample set in a preset region based on the rotor motion equation of the synchronous machine, wherein the sample set is a set of values of the state variable; initializing parameters of a neural network and an iteration number; 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 motion equation; inputting or setting running parameters of the neural network, wherein the running parameters comprise an input dimension, an output dimension, a hidden layer dimension, a learning rate, and a maximum iteration number, the input dimension is obtained according to the rotor motion equation of the synchronous machine, and the output dimension is obtained according to the output scalar function; acquiring an activation function of the neural network; running the neural network based on the running parameters, the parameters of the neural network, the iteration number, the activation function, the output scalar function, and the output risk function, and obtaining an output function; obtaining the Lyapunov function of the synchronous machine based on the new energy power system according to the output function.

5. The Lyapunov function based security stability analysis method of new energy power system according to any one of claims 1-4, characterized in that, The running step of the neural network comprises the following steps: Step 1: judge whether t < t max is established, in the formula, t is the iteration number, t max is the maximum iteration number: if not, modifying the preset region or the sample set; if yes, running the neural network; 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: judging whether the output function meets an output verification condition: if the output function does not meet the output verification condition, setting t=t+1, and repeating the steps 1 to 2; if the output function meets the output verification condition, the output function is the Lyapunov function.

6. The Lyapunov function based security stability analysis method of new energy power system according to any one of claims 1-5, characterized in that, The output risk function is: In the formulae: where L is the output risk function, x is the value of the state variable, θ is the parameter of the neural network, N is the total number of samples, s is the sample serial number, x s is the value of the state variable of the s th sample, f is the function corresponding to the synchronous machine rotor motion equation, For the partial derivative with respect to x, T denotes the transpose, hi is a constraint function of V, h2 is a constraint function of For output scalar function, m1 is the edge distance of output function from the origin, m2 is the edge distance of derivative of output function from the origin, m1 > 0, m2 > 0, V is the output function, The derivative of the output function.

7. The Lyapunov function based security stability analysis method of new energy power system according to any one of claims 1-5, characterized in that, The step of judging whether the output function meets the output verification condition comprises the following steps: based on a solver, obtaining a verification function from the sample set and the output function, the verification function being; where: Φ is a verification function, N is the total number of samples, s is the sample number, x s is the value of the state variable of the s-th sample, ε is a small constant parameter limiting the tolerable numerical error, x is the value of the state variable, V is an output function, εεQ + , Q + is a set of positive rational numbers; solving the verification function by using the solver, and judging whether the verification function is true; if the verification function is not true, the output function does not meet the output verification condition; if the verification function is true, the output function meets the output verification condition.

8. The Lyapunov function based security stability analysis method of new energy power system according to any one of claims 1-7, characterized in that, When the verification function is not established, the state variable value of the output function not satisfying the output verification condition is obtained according to the verification function, the state variable value of the output function not satisfying the output verification condition is added to the sample set, and the sample set is updated; the sample set is updated based on the sample set when the step 1 to the step 2 are repeated.

9. The Lyapunov function based security stability analysis method of new energy power system according to any one of claims 5-8, characterized in that, The output verification condition is: V(0) = 0 and V(x) > 0 in D - {0}, where V is an output function, x is a value of a state variable, and D is a predetermined region, The derivative of the output function. 10.The Lyapunov function based security stability analysis method of new energy power system according to claim 4, characterized in that, The hidden layer dimension is 7.

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