Reduce–factor–solve for fast Thevenin impedance computation and network reduction

Abstract

The complexity and volatility of power system operation increases when larger parts of the power production is based on distributed and non-controllable renewable energy sources. Ensuring stable and secure operation becomes more difficult in these modern power systems. For security assessment, the results of traditional offline simulations may become obsolete prior to the completion of the assessment. In contrast, real-time stability and security assessment aims at online computation, and it is therefore dependent on very fast computation of properties of the grid operating state. The paper develops the reduce-factor-solve approach to real-time computation of two key components in real-time assessment methods, network reduction and calculation of Thevenin impedances. The aim is to allow online stability assessment for very complex networks. The theoretical foundation behind the reduce-factor-solve approach is described together with the ability to handle both algorithms in a common framework. By exploiting parallelization of the reduce and solve steps in combination with fast matrix factorization, Thevenin impedances and reduced networks are computed much faster than previous approaches. The reduce-factor-solve algorithm is evaluated on power grids of varying complexity to show that Thevenin impedance computation and network reduction for complex power systems can be performed on a milliseconds time scale.

A Memory-Efficient Parallelizable Method for Computation of Thévenin Equivalents Used in Real-Time Stability Assessment

“…This means, that the entire coefficient matrix K is no longer needed, which will simplify the algorithm. The Thévenin impedances for cs and vs nodes are defined in (11). The diagonal of Z cs and the diagonal of the Schur complement Y eq is needed in these computations.…”

“…The method take advantage of a Schur complement, which [9] use to decompose the system for dynamic power system computations. In [5] a Schur complement is used to limit the computational burden when finding Thévenin equivalents for load buses, while [10] and the extended version of this [11] applies a Schur complement to efficiently compute Thévenin impedances for generators.…”

A Review of Parallel Heterogeneous Computing Algorithms in Power Systems

“…Following smart grids, contingency analysis is the next application where GPU is used to reduce the simulation time of power flow analysis [99][100][101][102][103][104][105][106][107][108]. Depending on the simulation time reduction achieved, hybrid CPU-GPU solutions can evaluate a high number of contingencies and scenarios to find an optimal performance of power systems.…”

Determination of the grid impedance in power consumption modes with harmonics

“…Another problem when investigating the impedance of an underground mining power supply system is that the loads can be highly variable at many connection points, and the harmonic system impedance can also be a non-stationary value. Approaches to determining harmonic system impedance in real time are described in [36,37].…”