## 1 Introduction  
The estimation of induction motor (IM) parameters is an essential research topic in the investigations on electrical drive systems, especially in the case of drives requiring high operational performance and precision. Modern control methods, such as the Direct Field Oriented Control (DFOC) and the Direct Torque Control (DTC) require the information about the internal state variables of the motor. Such signals as an electromagnetic flux, torque (or rotational speed for fully sensorless drives) cannot be measured directly, therefore they are estimated [1; 2; 3]. A major fraction of state variable estimators requires accurate knowledge about machine parameters [1; 4]. The most crucial parameters of the induction motor is stator winding resistance and rotor winding resistance which fluctuate due to temperature variations of the machine [5; 6]. Other important parameters encompass inductances, but they are immune to temperature variations [5]. The information about motor parameters values can be used also for the condition monitoring of machines [7; 8]. One of the used diagnostic methods is the assumption that the fluctuations of parameters can indicate a machine fault [9] (rotor bars rupture for squirrel-cage motors or stator windings short-circuit). Recently, numerous methods for induction motor parameters estimation have been developed. In general, they can be subdivided into two main categories [5]:  
* Off-line estimators--parameters are calculated at the standstill state of the machine (self-commissioning drives), these methods are often called parameters identification methods;
* On-line estimators--parameters are calculated during the normal operation of the machine. These methods are based mostly on: Kalman Filters [10], state observers [11], MRAS [5; 12] or spectral techniques [5]. The paper discusses MRAS based estimators, therefore in the further part of the introduction a brief description of this estimation method is given. A typical MRAS estimator (Figure 1) includes two basic subsystems which calculate the same base signal in different ways [12] (the same base signal is expressed by two mathematical models):  
* Reference model which should be independent of the estimated parameter;
* Adjustable model which is directly (sometimes indirectly) influenced by the estimated parameter. The general idea of this estimation algorithm relies on the minimization of the error between a reference and adjustable model by an adaptation mechanism. If the estimated parameter is equal to its reference value, the error becomes minimized. From the base signal standpoint, MRAS type parameter estimators can be classified into several major categories:  
* Electromagnetic flux-based (F-MRAS)--proposed for the first time in [13] for speed estimation. An estimator of this type can be used in stator resistance [14] or rotor resistance estimation [15], due to the fact that it consists of two basic estimators of the flux: a voltage model and a current model. The former depends directly on the stator resistance value, therefore it is used as an adjustable model in F-MRAS stator resistance estimators (in that case the current model is the reference). The current model depends directly on the rotor resistance, hence it is used as an adjustable model in F-MRAS rotor resistance estimators (then the voltage model is the reference). The major shortcomings of F-MRAS estimators are that neither of the models is a measurable quantity; estimators directly depend on both resistances simultaneously, however, only one of them can be estimated. * Reactive power-based (Q-MRAS)--proposed in [16] for rotor resistance estimation. This estimator is independent of stator resistance. It is implemented mainly in a synchronous reference frame (\(x\)-\(y\)), which requires the estimation of synchronous speed. The reference and adjustable models use internal signals from the control structure as inputs. Quite frequently, a simplified adjustable model is used (based on control method assumptions).