## [W-MB-167] Motor Plant Model Considering AC Loss for Control Calibration

Contents
1. Introduction
2. AC loss modeling
3. Control calibration Example: Current Vector Calibration for Maximum Efficiency Control
3.1 Motor and Control Specifications
3.2 Plant model specifications
3.3 Calibration method of the current command value
3.4 Calibration result
4. Summary
5. References

### 1. Introduction

Control parameter calibrations on Model-In-the-Loop Simulation (MILS) with Finite Element Analysis (FEA) based motor models is expected to be a standard procedure in the Model-Based-Design (MBD) for motor drive system developments. Although current standard motor models of electric machines can be used to see its basic behavior, the accuracy is not enough for the control parameter calibrations, especially for the estimations where AC loss in solid conductor windings is not ignorable. In this paper, the motor plant model considering AC loss is presented and applied for the control calibration of a PMSM maximum efficiency control.

### 2. AC loss modeling

A PMSM with solid conductor windings is focused herein. A voltage equation for a phase of a PMSM is written as (1) where $$V_i, \ R_i, \ I_i \ and \ \phi_i$$ are voltage, resistance, current and flux linkage of phase i, respectively. The iron loss can be included by adding an equivalent resistance in parallel with the second term on the right hand side of (1).
In order to take account of the AC loss, $$R_i$$ is replaced with the Cauer circuit which can represent reactions by eddy currents in a conductor. The inductance and resistances in the Cauer circuit are calculated by the analytical method.

$$V_i = R_iI_i + \frac{d\phi_i}{dI_i}$$　　(1)

### 3.1 Motor and Control Specifications

Fig. 1 and Table 1 show the cross-section and specifications of the motor. Fig. 2 shows the control model. The current vector is controlled by the PI control. The current vector, which is the command value, is selected so that efficiency is maximized at each operating point by calibration.

Fig. 1 Cross-section of the motor

Table 1 Motor specifications

 Objective functions 8/48 Core material 35JA300 Magnet NdFeB, Br=1.2 (T) Output 80 (kW) DC Voltage 600 (V) Maximum current 250 (A) Carrier frequency 6 (kHz)

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