通用感应电机高频特性综合模型及其验证

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本文档主要探讨了"通用感应电动机模型频率特性由低向高跳变特性"这一主题，发表在2007年9月至10月的IEEE Transactions on Industry Applications Vol.43, No.5上。作者Behrooz Mirafzal、Gary L. Skibinski、Rangarajan M. Tallam、David W. Schlegel和Richard A. Lukaszewski均为IEEE会员，他们共同提出了一个全新的三相感应电机模型，旨在描绘电机在宽广频率范围（从10Hz到10MHz）内的行为。该模型的独特之处在于它的普遍性，它将常见的共模(CM)、差分模(DM)以及轴承电路模型整合进一个统一的三相等效电路模型中。这与传统的低频IEEE Standard 112电路模型有所不同，但在此基础上进行了扩展，以便更好地适应高频环境下的性能分析。模型的开发旨在解决工业应用中的挑战，如轴承电流、电磁干扰(EMI)、高频率响应、PWM电压源逆变器的效应、反射波以及瞬态过电压等问题。作者通过实验模拟和验证了这个模型，展示了其在实际运行中的准确性和有效性。这种模型对于设计和控制感应电机系统，特别是在高频操作时，具有重要意义，有助于提高系统的效率、稳定性和抗干扰能力。对于从事电机工程、电力电子、自动化控制或EMI管理的人来说，理解和掌握这种新型频率特性模型是提升技术理解和应用的关键。研究结果对于理解电机在不同频率下性能的变化规律，优化电力系统设计，降低电磁兼容问题，以及开发更高效的驱动技术具有深远的影响。此外，由于现代工业环境中设备的高频化趋势，这项工作对于推动电机技术的未来发展具有战略价值。

MIRAFZAL et al.: INDUCTION MOTOR MODEL WITH LOW-TO-HIGH FREQUENCY-RESPONSE CHARACTERISTICS 1235

versus frequency of both 5- and 20-hp motors for a 460-V stator

winding connection only.

Fig. 1 demonstrates that the motor stray capacitors are mainly

a function of motor geometry. Low-frequency motor impedance

values below the ﬁrst resonance are mainly L–R equivalent

circuits. In this region, the impedance of the series 460-V

connection has four times the value of the parallel 230-V

connection since a winding inductance varies as N

(see Fig. 1

at 100 Hz). Fig. 1 also shows that the ﬁrst resonance frequency

of the 5-hp series connection is almost half the resonance

frequency (f

) of the parallel motor connections.

The f

of the motor impedance is deﬁned as where the

impedance has its maximum magnitude and is calculated by

=1/(2π

√

LC), where L and C are the effective inductance

and capacitance values, respectively. The effective inductance

L for a series connection is four times the value in a parallel

connection, and f

is half that of the parallel connection.

Accordingly, the conclusion is that the motor stray capacitance

does not signiﬁcantly vary with changes in stator winding

conﬁguration. That is, in this case, the effective capacitance

value C is mainly a function of the motor geometry or the

motor frame size. It will be shown in Section IV that Y- and

∆-connections have impacts on the equivalent capacitance

value at high frequencies.

The second objective of this section is to introduce the low-

impedance antiresonance phenomenon observed in the case of

the 20-hp motor at 4.1 MHz in Fig. 2. The motor impedance

at this resonance frequency is 10 Ω. This DM low impedance

at 4.1 MHz will be approximately equivalent to 2.2 Ω in the

CM circuit. This provides a very low impedance path for the

CM leakage current at the low-impedance antiresonance. Thus,

modeling of this phenomenon is of signiﬁcance for EMI analy-

sis in long cable motor drive systems. It is shown later that the

so-called antiresonance is actually caused by the inductance of

the ﬁrst few turns of the winding. These observations are further

discussed in Section IV, where the proposed motor model is

derived based on the IEEE Standard 112 (T-equivalent) circuit.

B. Testing of DM Transfer Function

DM testing was performed with the phase-A motor lead

as one probe and the phase-B and phase-C motor leads tied

together to form the second probe. The measurements were

taken using HP4284 (20 Hz to 1.0 MHz), HP4285 (75 kHz to

30 MHz), and AP200 (20 Hz to 15 MHz) LCR meters in Z–θ

(impedance magnitude and phase angle) mode [33], [34]. The

recommended test procedure is to use an ungrounded motor

frame. It was observed that grounding the motor frame resulted

in signiﬁcant measurement errors at high frequency. This is

attributed to errors in the instrument’s impedance calculation

procedure due to the LCR meter’s two-lead source voltage

driving capacitive current to ground that does not return on the

two leads [35].

C. Testing of CM Transfer Function

CM testing was performed with the motor frame as one probe

and the phase-A,-B, and -C motor leads tied together to form

Fig. 3. IEEE 112 recommended per-phase low-frequency equivalent circuit.

the second probe. Impedance measurements versus calculated

DM and CM transfer functions using the proposed induction

motor model are demonstrated later in Section IV-E.

III. M

ODELING INDUCTION MOTOR

FREQUENCY RESPONSE

In this section, existing lumped- and distributed-parameter

models for the analysis of the low- and high-frequency behavior

of induction motors are described.

A. Low-Frequency Response of Induction Motor

The low-frequency response of the polyphase induction mo-

tor has historically been studied since its origin. The IEEE

Standard 112 was established to obtain test methods and pa-

rameters for a low frequency (50, 60, and 400 Hz) per phase

T-equivalent induction motor model in Fig. 3 [36]. The rotor

circuit and neutral are actually physically isolated from the line

side stator neutral by the air gap in Fig. 3. Also, the rotor fre-

quency (slip frequency) is different from the stator (or line) fre-

quency. Users desire this low-frequency transfer function model

to obtain the line side electrical quantities (frequency, current,

power factor, and efﬁciency) for the given mechanical output

quantities (power, horsepower, and torque). For convenience of

analysis, rotor electrical quantities have thus been referred by

stator-to-rotor turns ratio to the stator with an implied electrical

connection to the stator neutral. In the low-frequency range,

the applied voltage is uniformly distributed through the stator

winding coils. Substantial literature exists on obtaining these

model parameters from mathematical calculations, heuristic

equations, and ﬁnite-element analysis (FEA). IEEE Standard

112 is a universally accepted test method to verify the ac-

curacy of these model parameters that are readily obtainable

by all users.

B. Mid-Frequency Response of Induction Motor

An accurate mid-frequency response (400 Hz to 20 kHz), as

related to PWM ac drives, would be correlated with the carrier

frequency motor ripple current and its associated heating in the

motor copper and core laminations.

C. High-Frequency Response of Induction Motor

The high-frequency response of the polyphase induc-

tion motor has recently been studied. High-frequency motor

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