This paper introduces the instantaneous energy function method, analyzes the instantaneous stability of single machine infinite power system, and expounds the application of the instantaneous energy function method. Keywords: instantaneous energy function method; Critical energy; Stability; stability

When the synchronous generator runs stably in the power system, because the mechanical power input by the prime mover is balanced with the loss and electromagnetic power output of the generator itself, the generator runs stably at synchronous speed and constant rotor angle. When the system is greatly disturbed, such as short circuit or sudden load change, the output power of the generator will suddenly change. Because the speed regulating device of the prime mover has considerable inertia, it takes some time to adjust the output power of the prime mover. Therefore, the power balance between the generator and the prime Mover is destroyed, and the unbalanced torque appears on the shaft of the unit, which changes the speed and power angle of the generator, causing the electromechanical transient process of the whole power system, and may even make the generator out of step. The problem of instantaneous stability is to discuss whether synchronous generators can keep synchronous operation after power system disturbance. 1 instantaneous energy function (Lyapunov function) Lyapunov function method is developed from the concept of classical mechanics: "For a free dynamic system (a system without external force), if the change rate of the total energy w [w (x) > 0, x is the system state variable] with time is always negative, it shows that the total energy of the system is decreasing continuously until it reaches a minimum value, then the system is stable." Lyapunov developed a strict mathematical tool to judge the stability of the system. This method looks at the stability problem from the perspective of energy and transformation, so it can quickly analyze the stability of the system. 1. 1 Its definition of stability and mathematical description of nonlinear systems with N-dimensional variables. According to the state variable method, the state variable equation of this system can be defined as a set of first-order ordinary differential equations expressed by state variables. Is it fresh or slow? This system is called autonomous system (infinite dynamic system is autonomous system). Then the above formula can be expressed as a stability discriminant theorem: (1) stability theorem: if there is a scalar function (energy function) w (x) in a neighborhood near the origin (new equilibrium point after troubleshooting), = dw/dt > 0 and x = 0；; When X≠0 is less than 0, the system is stable at the origin. ? 2) Asymptotic stability theorem: If there is a scalar function w (x) > 0 in a neighborhood near the origin, and there is < 0 in this neighborhood, then the system is asymptotically stable at the origin. ? 3) Asymptotically stable region theorem: Let ω be the solution region containing the origin, w (x) > 0, < 0, then all motions in ω region converge to the origin at t→∞. The basic application of 1.2 is to determine the number of state variables n of the system by the energy storage elements of the system, and then construct the energy function W(X) of the system (Lyapunov did not propose the method of constructing the energy function), and establish the stability region, that is, establish the critical energy Wr as the upper limit of the stability boundary, and take [wr-w (x)] as the quantitative description of the system stability, so as to queue up according to the severity of the accident and achieve the dynamic purpose. So how to construct energy function and critical energy is the key to the problem. Once the energy function is determined, the instantaneous stability of the system after troubleshooting can be directly judged by the above theorem according to the properties of the function. 2 transient stability analysis of single machine infinite system 2. 1 establish the mathematical model of single machine infinite system. The energy change of synchronous generator is reflected in the movement change of rotor, and the dynamic situation of synchronous motor can be described by the motion equation of rotor. Has a power angle δ. The difference between rotor angle and synchronous speed δ = dδ/dt is taken as the state variable. In the transient process, the rotor motion equation of synchronous motor is expressed as: where J is the moment of inertia of the rotor, K is the damping coefficient, M(t) is the algebraic sum of torques acting on the rotor, Mm(t) is the mechanical torque acting on the rotor by the prime mover, and Me(t) is the electromagnetic torque. Where ω is the difference (slip) between the rotor angular speed and the synchronous speed; Delta-generator rotor angle (power angle), expressed in electric radians; H—— inertia time constant of generator rotor, h = j/ (at the moment of TN fault removal, the potential energy of generator rotor is: in general, if the power angle corresponding to fault removal is δ and the power angle corresponding to the new stable equilibrium point is δS, the energy function is: it can be proved that the energy function satisfies Lyapunov stability theorem and asymptotic stability theorem. 2.3 After fault removal, the critical energy in the system is established, and there is an unstable equilibrium point U (the corresponding power angle is δU). The generator can only run to this point through the area where the system energy is reduced (PM < PE3, that is, the energy absorbed by the power grid), as shown in Figure 2-2, area B. If the total instantaneous energy W of the system at the moment of fault removal has been absorbed before reaching point U, the rotor will oscillate back and forth around point S, and finally, If instantaneous energy is absorbed just when it reaches point u, it is in equilibrium at that point. If the instantaneous energy is not absorbed when it reaches the U point, the residual energy will make the system cross the U point, the rotor will accelerate further and the generator will lose stability. It can be seen that the U point is the critical point, and the energy absorbed by the power grid in Area B is set as the critical energy Wr, so the system is stable, because both the energy function W and the critical energy Wr contain the same area, as shown in the figure, Area C. If the equation about the variable δ is solved, the square root δg is the upper limit of the stable area, and the stable area is 0 ~ δ g. Conclusion The energy function method does not need to calculate the whole transition process, but only needs to cut off the power angle and speed difference when the fault occurs. On this basis, the total energy and critical energy of the system are calculated, and the instantaneous stability of the system is determined according to the stability, thus greatly reducing the calculation amount. In this paper, the damping effect of the system is not considered, and the stability value can be reduced after considering the damping effect.