Estimation of inter-area oscillations in the Nordic power system using dynamic mode decomposition

Abstract

Abstract Electrification plays an important part in reducing greenhouse gas emissions to halt climate change, but creates growing demand for electric power. At the same time as electric power generation must be increased to meet this demand, the electric power industry must also transition to more climate-friendly energy sources. Therefore a large share of the power will have to come from converter-based generation such as wind and solar in the foreseeable future. Stability issues in the electric power system are likely to arise because converter-based generators do not contribute to the inertia of the power system. One stability issue which may become bigger in a low-inertia power system is inter-area power oscillations, which happen when synchronous generators in different geographical areas start to swing against each other. Inter-area oscillations already limit the transmission capacity of certain transmission corridors in the Nordic power system. Dynamic mode decomposition (DMD) is an algorithm for oscillation detection which has been noted as promising for power-system monitoring in several studies. However, a lot of research remains on the parameterisation of this algorithm and analysis of its estimation capabilities. This project provides validation of the algorithm’s ability to recognise known structures in data. Statistical tests were performed to chart the noise-sensitivity of DMD with respect to changes in sampling rate, data shift-stacking, the number of data channels, and the length of the analysis window. DMD was implemented with a randomised sampling technique and a rank selection method which had not been combined earlier, and which had not been tested for mode-tracking in PMU data over time. The algorithm’s performance was first tested on dynamic simulation data from the power-systems simulation software PSS/E. A user-defined load model was written to introduce stochastic consumption variations as a random walk in order to simulate ambient power-systems behaviour. DMD mode estimates were compared with results from stochastic subspace identification (SSI) and the multivariate autoregressive method (MAR), two algorithms which have already been in use by Nordic TSOs. DMD was found to give comparable results to SSI and MAR both under very noisy ambient conditions and on undamped oscillations after a disturbance, while having significantly lower computational cost. DMD, SSI and MAR were applied to tracking a mode in real-life PMU data from the Nordic power system under ambient conditions. Again DMD was found to give comparable results to SSI and MAR. A possible limitation in DMD’s ability to estimate the damping when using long analysis windows was identified.