Stable Equilibrium Point Calculation Using Pseudo-Transient Simulation
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Solution Overview
Problem
The existing methods for calculating stable equilibrium points in nonlinear dynamic systems, such as the Newton method and pseudo-transient simulation, often face convergence issues, leading to instability in power systems and requiring extensive computations, especially when initial values are not properly set or when high vibration properties are present.
Innovation Solution
Increasing the damping factor of the motion equation in a pseudo-transient simulation method for power systems, allowing for more stable and quicker convergence to equilibrium points, and using these values as initial conditions for the Newton method to determine stable equilibrium points.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the Newton method is used to calculate stable equilibrium points, then the calculation is simple and widely applicable, but numerical divergence occurs when initial values are not proper
Solution Approach 1:
The patent applies preliminary action by performing a pseudo-transient simulation before the Newton method to generate appropriate initial values. This preliminary simulation step prepares the system state in advance, ensuring that when the Newton method starts, it begins from a point where convergence is likely to occur, thus preventing numerical divergence while maintaining the simplicity of the overall calculation process.
2Reliability
If the pseudo-transient simulation method is used to find stable equilibrium points, then convergence can be achieved in cases where the Newton method fails, but the calculation time increases significantly
Solution Approach 1:
The patent uses preliminary action by running a pseudo-transient simulation for a limited duration (e.g., 0.1 to 1.0 seconds) to generate initial values, rather than running the full simulation. This preliminary step is sufficient to converge the initial values to a point where the Newton method can then quickly finish the calculation, significantly reducing total computation time while maintaining convergence reliability.
Solution Approach 2:
The patent segments the calculation process into two distinct phases: a pseudo-transient simulation phase for a limited time to generate initial values, and a Newton method phase to complete the calculation. This segmentation allows each method to operate in its optimal regime, with the simulation providing robust initial values and the Newton method providing rapid convergence, thereby reducing overall calculation time.
3Measurement precision
If the integral time step in pseudo-transient simulation is increased to reach stable equilibrium point vicinity, then convergence can be achieved, but the system may appear to have no stable equilibrium point when actually it does
Solution Approach 1:
The patent applies preliminary action by running the pseudo-transient simulation for a predetermined short duration to generate initial values, then using these initial values to start the Newton method. This approach ensures that the simulation doesn't run long enough to potentially miss the equilibrium point vicinity, but long enough to provide convergent initial values, thereby accurately detecting stable equilibrium points without false negatives.
Data Source
AI summary
In the present invention, in a case where a stable equilibrium point calculation is not calculable by using a Newton method, a damping factor of a mechanical system differential equation of a generator is set to be greater than an actual value of the generator of the power system. By applying pseudo-transient simulation to the nonlinear differential algebraic equation of the power system including the mechanical system differential equation of the generator, in which the damping factor is set, a norm of a mechanical system equation is found. If the found norm meets a predetermined condition, variable values of the power system at a time when the norm is found are set as initial values of the nonlinear differential algebraic equation of the power system. A stable equilibrium point is determined by applying the Newton method to the nonlinear differential algebraic equation in which the initial values are set.