# Identifying PMSM Motor Parameters with a Power Analyzer

## This article introduced a method for identifying PMSM motor parameters with a power analyzer easily yet with a high degree of precision.

*To boost overall efficiency of inverter and motor, it is necessary to measure power and motor parameters simultaneously because it is essential to verify the performance accurately to optimize the control parameters. The power analyzer PW6001 provides a new level of processing performance required to execute most accurate power measurement over a wide bandwidth and simultaneously identify various fundamental control parameters in the pursuit of high-efficiency power conversion with a power analyzer. *

Focusing on vector controlled PMSM, this article explains the effectiveness of these measurements.

## Background

Electric Motor Driven Systems (EMDS) are currently responsible for 53 % of global electricity consumption (IEA 2017) [1]. Herein, the worldwide electric car deployment will grow rapidly in the next one or two decades, and electric vehicles supposedly become the main source of demand growth in the sustainable development scenario. Consequently, the development of more efficient motor drive systems, is one of the important technologies in the strive to reduce the global energy demand. Continuous improvement of motor efficiency of inverter-controlled motors is a key objective and vector control of Permanent Magnet Synchronous Motors (PMSMs) is a commonly adopted technique to realize high-efficiency power conversion.

## Accurate solution using innovative power analyzers

In pursuit of overall improved power conversion efficiency, highly accurate power analysis and simultaneous analysis of motor parameters are required to validate optimized control parameters. This can be realized with highly accurate power analyzers deriving various parameters as shown in the evaluation image for motor control efficiency of Figure 1.

*Figure 1: Evaluation system for motor control efficiency with Power Analyzer PW6001*

Simultaneous calculation of power and motor efficiency that is regarded as standard nowadays, has been one of many newly introduced features and applications that Hioki has continuously been developing over more than 30 years in pursuit of a more precise power analysis. This was also resulted in the development of a wide range of Hioki high-accuracy current sensors.

When a power analyzer is adopted in a high precision power measurement application at higher frequencies, current sensors are typically used to accurately measure currents, but every current sensor in the world exhibits a gradually increasing phase error at the highfrequency region. This is due to the nature of current transformers and delay of subsequent electronic circuitry. Hioki put its know-how of current sensors into the design and production process to suppress variations of phase delay of individual sensors and the PW6001 has an integrated current sensor phase shift correction function that achieves a more accurate power analysis over a wide bandwidth [Figure 2].

*Figure 2: Phase error with and without compensation*

In addition, a newly developed “Power Analysis Engine” adds the enhanced high-performance processing power to perform oscilloscope-like waveform analysis, as well as power and motor analysis with leading measurement accuracy, a wide measurement bandwidth, and measurement stability. In regards to motor analysis, although a variety of high-performance control methods have been proposed for PMSMs, accurate identification of motor and control parameters such as d-axis inductance Ld, and q-axis inductance Lq, in d-q equivalent circuits is essential to optimize motor control parameters. Correct measurement of electrical angle, d-q axis voltage and current using a harmonic analysis is the method to identify these parameters.

## Measurement principles

In general, power analyzers create folding noise by aliasing, which can be reduced by anti-aliasing filters (AAF). [Figure 3(a)]. However, AAFs limit wide band measurements. The newly developed “Power Analysis Engine” realizes optimal data sampling and analysis with AAF that rejects higher frequency components than Nyquist frequencies from the input wave form [Figure 3(b)]. It also enables accurate harmonic analysis with optimal sampling speed simultaneously with subsequent independent Zero-cross filter and AAF.

*Figure 3(a): Example: 5MHz sampling without AAF*

*Figure 3(b): Independent AAF and synchronization*

Consequently, these configurations of AAF offer 2 MHz bandwidth measurement without aliasing noise and this level of harmonic analysis accuracy enables accurate power and efficiency measurements. In addition, accurate and steady measurement of fundamental frequency components of power parameters realizes to derive motor and control parameters correctly.

## Identification of motor and control parameters

In general, PMSM analysis and control are based on the equivalent circuit model for a motor expressed on the d- and q-axes. Although a variety of high-performance control methods have been proposed for PMSMs, and these control algorithms are based on d-q equivalent circuits with motor parameters such as d-axis and q-axis inductance, Ld and Lq.

When a steady state is considered, a vector diagram of the d- and q-axis is expressed as shown in Figure 4. Here, v1 and i 1 represent the fundamental wave components of the phase voltage and phase current, while ϑv and ϑi represent the fundamental wave phase angle of the phase voltage and phase current respectively. From here the control parameters equation (1)-(4) can be derived by user defined function (UDF) with a power analyzer as equation (5)-(8). vd = -v1 sinϑv (1) UDF1 = -Ufnd1 sinϑU1 (5) vq = v1 cosϑv (2) UDF2 = Ufnd1 cosϑU1 (6) i d = -v1 sinϑi (3) UDF3 = -I fnd1 sinϑI1 (7) i q = v1 cosϑi (4) UDF4 = I fnd1 cosϑI1 (8)

*Figure 4: PMSM Vector Diagram*

Here, Figure 4 and equations (1)-(8) are expressed based on the following assumptions [2].

- The spatial distribution of magnetic flux in the spaces between the stators and rotors takes the form of a sine wave aligned with the gap.
- The harmonic components of voltage and current can be ignored.
- The core loss can be ignored.

Using equations (1)-(8) and Figure 4, motor parameters Ld and Lq can be derived and determined by UDF in a power analyzer as follows:

$$Ld \ : \ UDF_7 \ = \ \frac{UDF_2}{2 \pi f_1 \cdot UDF_3} - \frac{2 \pi Kef_1 + R \cdot UDF_4}{2 \pi f_1 \cdot UDF_3} \ \ \ \ (9)$$

$$Lq \ : \ UDF_8 \ = \ \frac{R \cdot UDF_3 - UDF_1}{2 \pi f_1 \cdot UDF_4} \ \ \ \ (10)$$

The induced voltage constant Ke and the phase armature resistance R can be obtained as follows.

For inducing Ke ([3], [4]), place the motor terminals of the PMSM being analyzed in the open state (i d = i q = 0), connect the motor terminals to the “CH 1”, “CH 2”, and “CH 3” voltage inputs on the power analyzer. Then connect the encoder’s A-phase pulse output to “CH B”, the B-phase pulse output to “CH C”, and the Z-phase pulse (origin signal) output to “CH D” (Figure 5).

*Figure 5: Wiring for phase zero-adjustment and induced voltage constant Ke identification.*

Configure the power analyzer by setting the motor analysis operating mode, the measurement parameter to “Torque, Speed, Direction, and Origin ”, and “CH B” input to “Pulse”. Then set the wiring for “CH 1”, “CH 2”, and “CH 3” to “3P3W3M”, the synchronization source to “Ext1”, and ∆ - Y conversion to “ON”. Setting the synchronization source to “Ext1” allows the voltage and current phase angles to be measured using the inputted encoder pulse as the reference, and setting ∆ - Y conversion to “ON” allows the line voltage to be converted to, and measured as a phase voltage.

Operate the motor from the load side in this state to generate an induced voltage and perform phase zero-adjustment on the power analyzer. This step will ensure that v and i represent phase angles (I.e. electrical angles) based on the phase of the induced voltage generated along the q-axis.

At this time, the induced voltage vq will equal to v1 and Ke is identified by equation (11).

$$Ke = \frac{V_1}{2 \pi f_1}$$

The phase armature resistance R can be measured by a resistance meter with the 4 terminal method.

The motor torque is calculated by following equation (12).

$$T = Pn \{Ke \ iq + (Ld-Lq) id \ iq \} \ \ \ \ (12)$$

**Pn** is number of motor pole pairs.

The first term on the right side is magnetic torque, and the second term is the reluctance torque. Magnetic torque is generated by attraction and repulsion force between the rotating magnetic field of the stator and the permanent magnet rotor.

Then, drive the motor by invertor under test to measure motor and control parameters. Measured results are displayed as follows:

Figure 6 shows the calculated and measured torque. Calculated torque is derived by equation (12) with use of derived motor parameters (Ld, Lq), control parameters (id, iq) and Ke, and it fits well with the measured torque. This also means that motor torque can be identified without a torque sensor in case it is not possible to adopt a torque sensor into utility drive system.

*Figure 6: Comparison of measured and calculated torque*

Figure 7 illustrates the results of identifying the Ld and Lq motor parameters while the motor’s rpm varies and the current phase angle is held constant, showing the current dependence of Ld and Lq. Ld remains roughly constant regardless to id. By contrast, Lq exhibits a high degree of current dependency due to magnetic saturation and varies significantly with iq. These characteristics exemplify that it is not possible to use an LCR meter or similar instrument to identify Ld with a high degree of precision while the motor is at a standstill. Instead, the value must be identified while the motor is operating.

*Figure 7: Relationship between the d-q axis current and the identified d-q axis self-inductance*

In this article, we introduced a method for identifying PMSM motor parameters with a power analyzer easily yet with a high degree of precision. As an analytical model, we assumed that core loss can be ignored. However, by measuring mechanical loss and identifying the equivalent core loss resistance in advance, it would be possible to develop the described method for identifying motor parameters while taking core loss into account. This would be a next step for us to identify core loss in electric drives.

## Conclusion

With a high level of processing power, actual motor parameters can be identified simultaneously with accurate power measurement when executing this method with the HIOKI Power Analyzer PW6001. The power analyzer’s enhanced functions therefore enable effective research on vector control technology of PMSM motors to aim for ever more efficient power conversion, and ultimately contribute to finding solutions how to decrease energy consumption on a larger scale.

#### About the Authors

**Hidekazu Masuda** is a senior staff at Hioki E.E. corporation, which HIOKI is a electrical measuring instruments company that comprise four product groups: automatic test equipment, data recording equipment, electronic measuring instruments, and field measuring instruments. Collectively, these products are used in an extensive range of industries and fields, from research and development to facility and equipment maintenance and service.

**Shozo Yoda** holds a Ph.D. in Engineering at Shinshu University, a Master's and Bachelor's Degree in Electronics Engineering both at the University of Electro-Communications. He currently works as the Product Manager at Hioki Europe GmbH since January 2018.

#### References

- International Energy Agency: World Energy Outlook 2016, IEA Paris 2016
- Shigeo Morimoto, Yoji Takeda, and Takao Hirasa: “Method for Measuring a PM Motor’s dq Equivalent Circuit Constants”, IEEJ Transactions on Industry Applications, Vol.113-D (1993) No.11, pp.1330-1331 (in Japanese)
- HIOKI white paper: “Identification of PMSM Parameters with the Power Analyzer PW6001(Theory and setting apparatus)”, 2015 https://www.hioki.com/file/cmw/hdTechnicalDataEn/53/attached_ file/
- HIOKI white paper: “Identification of PMSM Parameters with the Power Analyzer (Actual measurements)”, 2016

This article originally appeared in the Bodo’sPower Systems magazine.

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