解耦分析建模方法
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It is relatively difficult to derive an accurate mathematical model for SRM due to its doubly salient structure and saturated magnetic field, which result in strong nonlinearities in flux-linkage and static torque characteristics [5]. However, for performance prediction and advanced control of SRM, an accurate model is critical.
Index Terms— Decoupled analytical model, dynamic performance, flux linkage, Fourier series, switched reluctance machine (SRM).
I. INTRODUCTION
In this paper, a new method to calculate the flux-linkage
analytical modeling methods for SRM have been presented. In [10], an accurate modeling method for SRM is proposed based on exponential function. However, the least square method is adopted to obtain the coefficients, which is time consuming. In [11], the Fourier series in expression of current-dependent arctangent function is utilized to build the model of the SRM.
such as lookup table techniques [6], magnetic equivalent circuit analysis [7], neural network (NN) [8], and finite-
II. DECOUPLED ANALYTICAL MODELING METHOD
2
2
ψ(θ, i ) = a0(θ )+ am(θ ) cos(ω1mi)+ bm(θ ) sin(ω1mi)
m=1
m=1
(1)
ω1 = π/(imax − imin)
(2)
However, the coefficients in arctangent function cannot be directly calculated and the accuracy of the model depends on the method used for curve fitting. Effective modeling methods for SRM based on Fourier series are also proposed in [12] and [13], but the process to determine the coefficients of the series is relatively complex and/or needs numerous sample data.
There are several approaches to build the model of SRM,
and static torque characteristics of SRM is proposed based on Fourier series expansion. The complicated and nonlinear influences of phase current and rotor position on flux linkage are decoupled and a limited amount of sample data is required to determine the coefficients of the Fourier series. By the proposed formula, the flux linkage and static torque with any phase current and rotor position can be calculated easily. The validity of the proposed method is verified by comparison between calculated and measured characteristics. Finally, based on the characteristics obtained by the proposed method, the dynamic simulation model of SRM is built in MATLAB. The simulation results under different operation conditions are compared with those from experiments, and errors between them are fairly small, which further demonstrates that the proposed method is effective and accurate.
School of Automation, Northwestern Polytechnical University, Xi’an 710072, China
This paper proposes a new decoupled analytical modeling method for switched reluctance machine (SRM). The flux linkage is represented by a second-order Fourier series, and the coefficients of the series are position dependent, which can be further expressed by another second-order Fourier series. The proposed method only needs 21 data points from five rotor positions. Then, the static torque characteristics are analytically obtained based on the expression of the flux linkage. The accuracy of the method is verified by comparing the calculated flux-linkage and static torque characteristics with those from measurements. With the calculated flux-linkage and static torque data, the dynamic performance of SRM is simulated under both motoring and generating mode. The simulation results, such as phase current and mechanical characteristics, agree well with those from the experiment, which further proves the effectiveness of the proposed method.
where coefficients am and bm are constant for a given position and can be calculated with the flux-linkage data. imax and imin are the maximum and minimum phase current in the measured
S WITCHED reluctance machine (SRM) has simple and rugged structure, high efficiency and reliability, wide speed range, flexible control, and low cost, and it is suitable for working in wenku.baidu.comarsh environment, such as high speed and high temperature. Due to these outstanding advantages, SRM has attracted increasing attention [1], and is competitive in many fields, including aviation industry, electric vehicle, wind power generation, household appliances, and so on [2]–[4].
To improve the utilization ratio of material, SRM always operates with certain saturation, which results in nonlinear electromagnetic characteristics. The flux linkage ψ(θ, i ) is a function of phase current and rotor position, which can be analytically presented by the following Fourier series:
data. The unit of rotor position θ is degree. In this paper, the
coefficients am and bm are calculated by another second-order Fourier series as follows, which is a function of θ :
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 3, MARCH 2015
8100504
A New Decoupled Analytical Modeling Method for Switched Reluctance Machine
Shoujun Song, Man Zhang, and Lefei Ge
element method (FEM) [9]. Magnetic equivalent circuit analysis and FEM are complex and time consuming and intensive computation is needed. The NN and lookup table techniques require numerous sample data from experiments or FEM, which inevitably takes much time. In some literature,
Index Terms— Decoupled analytical model, dynamic performance, flux linkage, Fourier series, switched reluctance machine (SRM).
I. INTRODUCTION
In this paper, a new method to calculate the flux-linkage
analytical modeling methods for SRM have been presented. In [10], an accurate modeling method for SRM is proposed based on exponential function. However, the least square method is adopted to obtain the coefficients, which is time consuming. In [11], the Fourier series in expression of current-dependent arctangent function is utilized to build the model of the SRM.
such as lookup table techniques [6], magnetic equivalent circuit analysis [7], neural network (NN) [8], and finite-
II. DECOUPLED ANALYTICAL MODELING METHOD
2
2
ψ(θ, i ) = a0(θ )+ am(θ ) cos(ω1mi)+ bm(θ ) sin(ω1mi)
m=1
m=1
(1)
ω1 = π/(imax − imin)
(2)
However, the coefficients in arctangent function cannot be directly calculated and the accuracy of the model depends on the method used for curve fitting. Effective modeling methods for SRM based on Fourier series are also proposed in [12] and [13], but the process to determine the coefficients of the series is relatively complex and/or needs numerous sample data.
There are several approaches to build the model of SRM,
and static torque characteristics of SRM is proposed based on Fourier series expansion. The complicated and nonlinear influences of phase current and rotor position on flux linkage are decoupled and a limited amount of sample data is required to determine the coefficients of the Fourier series. By the proposed formula, the flux linkage and static torque with any phase current and rotor position can be calculated easily. The validity of the proposed method is verified by comparison between calculated and measured characteristics. Finally, based on the characteristics obtained by the proposed method, the dynamic simulation model of SRM is built in MATLAB. The simulation results under different operation conditions are compared with those from experiments, and errors between them are fairly small, which further demonstrates that the proposed method is effective and accurate.
School of Automation, Northwestern Polytechnical University, Xi’an 710072, China
This paper proposes a new decoupled analytical modeling method for switched reluctance machine (SRM). The flux linkage is represented by a second-order Fourier series, and the coefficients of the series are position dependent, which can be further expressed by another second-order Fourier series. The proposed method only needs 21 data points from five rotor positions. Then, the static torque characteristics are analytically obtained based on the expression of the flux linkage. The accuracy of the method is verified by comparing the calculated flux-linkage and static torque characteristics with those from measurements. With the calculated flux-linkage and static torque data, the dynamic performance of SRM is simulated under both motoring and generating mode. The simulation results, such as phase current and mechanical characteristics, agree well with those from the experiment, which further proves the effectiveness of the proposed method.
where coefficients am and bm are constant for a given position and can be calculated with the flux-linkage data. imax and imin are the maximum and minimum phase current in the measured
S WITCHED reluctance machine (SRM) has simple and rugged structure, high efficiency and reliability, wide speed range, flexible control, and low cost, and it is suitable for working in wenku.baidu.comarsh environment, such as high speed and high temperature. Due to these outstanding advantages, SRM has attracted increasing attention [1], and is competitive in many fields, including aviation industry, electric vehicle, wind power generation, household appliances, and so on [2]–[4].
To improve the utilization ratio of material, SRM always operates with certain saturation, which results in nonlinear electromagnetic characteristics. The flux linkage ψ(θ, i ) is a function of phase current and rotor position, which can be analytically presented by the following Fourier series:
data. The unit of rotor position θ is degree. In this paper, the
coefficients am and bm are calculated by another second-order Fourier series as follows, which is a function of θ :
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 3, MARCH 2015
8100504
A New Decoupled Analytical Modeling Method for Switched Reluctance Machine
Shoujun Song, Man Zhang, and Lefei Ge
element method (FEM) [9]. Magnetic equivalent circuit analysis and FEM are complex and time consuming and intensive computation is needed. The NN and lookup table techniques require numerous sample data from experiments or FEM, which inevitably takes much time. In some literature,