A Semi-Analytical Framework for Faster Deterministic and Stochastic Power System Simulations

University Of Tennessee Knoxville, Knoxville TN

Investigators

Abstract

With the increasing penetration of intermittent and renewable resources, electric utilities are facing new challenges in computer simulation of interconnected power systems. These challenges include (1) how to handle the fast growing dimensionality and nonlinearity in mathematical models of power grids, and (2) how to deal with increasing uncertainties in daily grid operations. The increasing uncertainties stem from the varying and unpredictable nature of renewable energy sources such as solar and wind, and even from inaccuracy in the mathematical models of renewable sources. The so-called "faster-than-real-time simulation" of a power grid is expected to start as soon as a disturbance is detected and to conclude even before the impact ends so as to improve real-time situational awareness and decision support capability of the grid operator against major power outages and enable real-time stability assessment and control. However, the traditional numerical integration based simulation approach has little power to improve time performance for real-time implementation due to its mechanism of iterative computations. Stochastic simulations are becoming more important for power grids with a high penetration of renewables but have not been executed well using the traditional simulation approach. This project will explore a completely new direction to achieve faster power grid simulation in both deterministic and stochastic approaches. The proposed semi-analytical framework is a better fit for faster-than-real-time simulation on parallel computers and also for stochastic power system simulations involving renewable sources. Success of the project may inspire software vendors to apply this new semi-analytical methodology leading to faster power grid simulation tools to help reduce the risk of the power grid to blackouts. This new methodology for power grid simulation can be generalized for fast simulation of other large-scale nonlinear dynamic systems. Unlike the traditional simulation approach solving power grid nonlinear differential-algebraic equations by numerical integration and iteration, this new approach decomposes the solution process into tasks in two basic stages: the offline stage uses the Adomian decomposition method to derive an approximate, analytical solution called a "semi-analytical solution" (SAS) for each state variable, which is valid for a certain time interval and has symbolic variables such as the time, other state variables and parameters on the system condition; the online stage evaluates the analytical expression of each SAS by plugging in values of its symbolic variables for consecutive intervals until achieving the desired period of simulation, so the simulation result can be given in an extremely fast manner without any numerical integration or iteration. The project will take four steps to establish this semi-analytical methodology and its theoretical framework: (1) developing a systematic procedure to derive SASs for realistic power grid models; (2) studying the maximum potential of this new approach in fast deterministic and stochastic simulations; (3) implementing and testing this approach on a high-performance supercomputer; and (4) incorporating the approach with the traditional numerical approach into a hybrid approach under the recently studied "Parareal in Time" framework to explore the biggest potential in faster-than-real-time simulation for interconnected power systems.