Measurement of the flux is a very important task to control methods of electrical motors such as vector control and direct torque control. In sensorless speed control of induction motors, the position and speed of the rotor must be estimated from other parameters such a flux. In the operational phase the measurement sensors, especially current sensors which have measurement error values. Also, any change in motor parameters causes the flux not to be measured accurately and to be an estimate of the actual flux. Various methods have been proposed to the flux estimation, including voltage model based flux estimation, which involves integrating of the back-electromotive force called the pure integration, which has three problems: the saturation of the integrator due to the input DC component, the DC bias due to the initial conditions of the integrator and the harmonics. several methods have been proposed to solve these problems, such as the approximate integrator, which is a low-pass filter. This method does not have the pure integration saturation and can discharge the DC bias, but it causes amplitude and phase errors in the estimated flux that it requires a compensation, which it causes increasing the complexity of the system. The second-order generalized integrator as the approximate integrator can be eliminate the DC bias and further attenuation the harmonics rather than the two previous methods, although the DC component problem persists. In addition, this system requires the frequency of the input signal for its operation, if the frequency of the input signal is unknown, is estimated by a frequency locked-loop, which has an unfavorable performance in the presence of harmonics. The proposed method is a combination of a low-pass filter with a second-order generalized integrator structure called LPF - SOGI , which is more capable of harmonic attenuation as well as a more accurate and faster frequency estimation and is more resistant to noise, resulting in more accurate flux estimation. Although it does not have a positive effect on the DC component. The stability analysis of LPF - SOGI is based on the averaging and singular perturbation theorems. By replacing the moving average filter with a low-pass filter in the proposed system, MAF - SOGI emerges which compared to LPF - SOGI , can eliminate certain multiples of harmonics and the DC component. To remove most of the harmonic and DC components, sub-filters based on the moving average filter are introduced, which by combining with SOGI , LPF - SOGI , and especially MAF - SOGI , it can be claimed that with the lowest possible order, more destructive have been removed. Thus, LPF - SOGI and MAF - SOGI replace SOGI and can be used in network frequency estimation, telecommunication applications, power systems, and flux estimation. simulations confirm the performance of the proposed algorithms. Key Words: Second order generalized integrator, Low pass filter, Flux estimation, Frequency locked loop, Moving average filter, Singular perturbation.
