**Abstract**

The hydrodynamic instabilities in a turbomachine can be divided into two main groups: periodic (or quasi-periodic) and nonperiodic. And the total instability, calculated from a statistical parameter with linear characteristics, such as variance, can be defined as the sum of periodic and nonperiodic instabilities. Based on the above, the main objective of the study was to estimate the periodic instabilities in a pump operating as a turbine. For this purpose, pressure fluctuation signals from sensors installed on the turbomachine volute and spaced 135° apart were used. The signals were analyzed in the time and frequency domain to identify, initially, the periodic instabilities and their relationship with the spectral components and, subsequently, to estimate the magnitude of these instabilities as the variance of the filtered series in the spectral band related to the periodic instability. In addition, the study aims to establish the contribution of periodic instabilities to total instability.

**Keywords:** pump as turbine, hydrodynamic instabilities, periodic instabilities, variance, phase analysis, Fourier analysis
