On Accurate Discrete-Time Dynamic Models of an Induction Machine
Induction machines have become the standard for highly demanding industrial applications. This has led to the utilization of modern discrete-time control techniques (such as model predictive control) that require the estimation of internal variables that are not subject to measurement (such as the r...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/3/373 |
| _version_ | 1797318448797188096 |
|---|---|
| author | Ramón Herrera Hernández Carlos Reusser María Coronel Rodrigo Carvajal |
| author_facet | Ramón Herrera Hernández Carlos Reusser María Coronel Rodrigo Carvajal |
| author_sort | Ramón Herrera Hernández |
| collection | DOAJ |
| description | Induction machines have become the standard for highly demanding industrial applications. This has led to the utilization of modern discrete-time control techniques (such as model predictive control) that require the estimation of internal variables that are not subject to measurement (such as the rotational velocity in sensorless applications). From this point of view, it is fundamental to have accurate discrete-time models of induction machines, particularly given their nonlinear nature, so that control techniques perform according to design requirements. In spite of the above, the modeling of induction machines has not received much attention in the literature, even though more powerful machines and faster microcontrollers are currently being used. To better understand induction machine models for control, in this paper, we develop and compare various discrete-time models of induction machines based on Euler, Taylor, and Runge–Kutta methods. In addition, we compare the Extended Kalman Filter and Unscented Kalman Filter for state estimation in terms of accuracy and computational burden. The models are derived and compared through extensive Monte Carlo simulations and the state estimation techniques are compared in terms of root mean squared error, execution time, and maximum absolute error. Our simulations show that, in general, the Taylor method yields more accurate models than both the Runge–Kutta and Euler methods. In particular, the Taylor method results in a root mean square error that is one order of magnitude smaller than the Euler method for stator current and rotor flux linkages. For rotor angular speed, the Runge–Kutta methods are more accurate than both the Taylor and Euler methods, resulting in a root mean square error that is two orders of magnitude smaller than the Euler method. On the other hand, the Extended Kalman Filter results in smaller execution time than the Unscented Kalman Filter, up to two orders of magnitude. In terms of root mean squared error and maximum absolute error, both filtering algorithms perform similarly. |
| first_indexed | 2024-03-08T03:52:33Z |
| format | Article |
| id | doaj.art-3f9331735fca4ec48a5e01db096be035 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T03:52:33Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3f9331735fca4ec48a5e01db096be0352024-02-09T15:18:07ZengMDPI AGMathematics2227-73902024-01-0112337310.3390/math12030373On Accurate Discrete-Time Dynamic Models of an Induction MachineRamón Herrera Hernández0Carlos Reusser1María Coronel2Rodrigo Carvajal3School of Electrical Engineering, Pontificia Universidad Católica de Valparaíso (PUCV), Av. Brasil 2147, Valparaíso 2362804, ChileSchool of Electrical Engineering, Pontificia Universidad Católica de Valparaíso (PUCV), Av. Brasil 2147, Valparaíso 2362804, ChileDepartment of Electricity, Universidad Tecnológica Metropolitana (UTEM), Av. Jose Pedro Alessandri 1242, Santiago 7800002, ChileSchool of Electrical Engineering, Pontificia Universidad Católica de Valparaíso (PUCV), Av. Brasil 2147, Valparaíso 2362804, ChileInduction machines have become the standard for highly demanding industrial applications. This has led to the utilization of modern discrete-time control techniques (such as model predictive control) that require the estimation of internal variables that are not subject to measurement (such as the rotational velocity in sensorless applications). From this point of view, it is fundamental to have accurate discrete-time models of induction machines, particularly given their nonlinear nature, so that control techniques perform according to design requirements. In spite of the above, the modeling of induction machines has not received much attention in the literature, even though more powerful machines and faster microcontrollers are currently being used. To better understand induction machine models for control, in this paper, we develop and compare various discrete-time models of induction machines based on Euler, Taylor, and Runge–Kutta methods. In addition, we compare the Extended Kalman Filter and Unscented Kalman Filter for state estimation in terms of accuracy and computational burden. The models are derived and compared through extensive Monte Carlo simulations and the state estimation techniques are compared in terms of root mean squared error, execution time, and maximum absolute error. Our simulations show that, in general, the Taylor method yields more accurate models than both the Runge–Kutta and Euler methods. In particular, the Taylor method results in a root mean square error that is one order of magnitude smaller than the Euler method for stator current and rotor flux linkages. For rotor angular speed, the Runge–Kutta methods are more accurate than both the Taylor and Euler methods, resulting in a root mean square error that is two orders of magnitude smaller than the Euler method. On the other hand, the Extended Kalman Filter results in smaller execution time than the Unscented Kalman Filter, up to two orders of magnitude. In terms of root mean squared error and maximum absolute error, both filtering algorithms perform similarly.https://www.mdpi.com/2227-7390/12/3/373induction machineBayesian filteringdiscretization |
| spellingShingle | Ramón Herrera Hernández Carlos Reusser María Coronel Rodrigo Carvajal On Accurate Discrete-Time Dynamic Models of an Induction Machine Mathematics induction machine Bayesian filtering discretization |
| title | On Accurate Discrete-Time Dynamic Models of an Induction Machine |
| title_full | On Accurate Discrete-Time Dynamic Models of an Induction Machine |
| title_fullStr | On Accurate Discrete-Time Dynamic Models of an Induction Machine |
| title_full_unstemmed | On Accurate Discrete-Time Dynamic Models of an Induction Machine |
| title_short | On Accurate Discrete-Time Dynamic Models of an Induction Machine |
| title_sort | on accurate discrete time dynamic models of an induction machine |
| topic | induction machine Bayesian filtering discretization |
| url | https://www.mdpi.com/2227-7390/12/3/373 |
| work_keys_str_mv | AT ramonherrerahernandez onaccuratediscretetimedynamicmodelsofaninductionmachine AT carlosreusser onaccuratediscretetimedynamicmodelsofaninductionmachine AT mariacoronel onaccuratediscretetimedynamicmodelsofaninductionmachine AT rodrigocarvajal onaccuratediscretetimedynamicmodelsofaninductionmachine |