## 1 Introduction  
The three-phase AC induction asynchronous induction motors (with a squirrel-cage rotor) are currently widely used for driving mechanical systems, mainly due to their simplicity and reliability. Firstly, monitoring the condition of these motors with no load (idling) and detecting possible failure situations that could lead to a catastrophe is a major topic of scientific research. Secondly, understanding the behaviour of these motors allows their design and operation to be optimised. The signals taken into account when monitoring the condition of motors are among the most diverse. The valuable motor output signals provided by the motor and suitable for condition monitoring are acquired by means of appropriate sensors placed on the motor or on its rotor (most frequently vibration sensors [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12], temperature sensors [2; 3; 4; 5; 6; 13; 14; 15; 16; 17; 18], instantaneous rotation speed sensors [6; 9; 14; 16; 18; 19; 20; 21], acoustic sensors [5; 8; 11; 12; 14] and rarely magnetic field and flux sensors [20; 22; 23] or stray-flux sensors [6; 24]). The valuable motor input signals are often acquired from the electrical supply system using appropriate instantaneous voltage and current sensors. The most commonly used input signal in motor condition monitoring is the description of the absorbed current (e.g., by Motor Current Signature Analysis, MCSA [8; 9; 13; 14]), which has been widely used in scientific research [2; 4; 6; 7; 8; 9; 11; 12; 14; 15; 17; 18; 20; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35]. The use of voltage sensors is indirect and rarely used on its own, e.g., in unbalancing detection of an AC power supply and overvoltage detection [26], detection of broken bars in stator [13], to prevent phase loss [36] or to describe voltage waveform anomalies [2]). Otherwise, voltage sensors are almost always combined with the use of current sensors to provide other useful information and signals for monitoring, such as the description of the absorbed instantaneous electrical power or active electrical power [13; 19; 25; 34], as the subject of our previous research [21], the detection of the phase or phase shift of the instantaneous current [30; 33; 37], or the description of the power factor variation over time [6; 13; 17]. It is important to note that there is a strong correlation between the input signals (related to the absorbed electrical power and its components) and the output signals (generally describing mechanical phenomena), especially in the case of periodic phenomena, conditioned, of course, by the dynamics of the rotor rotating through the rotating magnetic field generated by the stator. The motor acts as an energy (power) transformer from electrical to mechanical form. Many normal and abnormal variable mechanical phenomena (e.g., related to bearing condition [1; 2; 10; 11], rotor mechanical imbalance/eccentricity [10; 28]) during motor operation (especially with no load) should be reflected (with an amplitude and the phase at the origin of time depending on the frequency) in the evolution of the current, the power factor and especially the instantaneous (and/or active) electrical power. The motor acts as a mechanical load sensor. The use of signals describing the variation over time of the electrical inputs in the motor offers a major advantage: simplicity of installation and use of the sensors (simple current and voltage transformers), sometimes with the possibility to use wireless data transmission [10; 17; 26]. There are many processing techniques available for condition monitoring of AC induction motors, most of which are used to extract useful information from variable (mainly periodic) signals.