Influence of temperature on power factor and operating area of SynRM machine in automotive equipment

ABSTRACT


INTRODUCTION
Besides being used for the main traction motor development, the integration of motors into other major functions of an automobile have seen many phases of improvement and optimization [1]- [3].In our study previously presented in [4]- [6], a synchronous reluctance machine (SynRM) machine was designed to operate as a clutch actuator, and placed inside the gear housing.The ambient temperature can reach up to 140 °C.The segmented rotor SynRM topology was chosen.The advantages of this topology of SynRM are that it is void of permanent magnets and the rotor is easy to fabricate for a small-size rotor [7].A more popular flux barrier SynRM [8] is here irrelevant due to the manufacturing difficulties of stamping a small flux barrier in the rotor, and the high possibility of having saturation around the barrier.The design, dimensions, and assembly of the prototype can be found in the Figures 1 and 2. Figuress 1 and 2 show the design, dimensions, and assembly of the SynRM prototype machine.The maximum torque load angle is at  = 45°.
Studies regarding its thermal behavior and losses were extensively done to ensure that the machine can cope with the load without damaging its winding insulation [6], [9] which is the only thermal-sensitive component in the machine.Tested for the WLTP speed profile, the clutch application shows that the SynRM temperature stays within the safe temperature range.Now that we are sure that the machine will not be damaged by the temperature, it is necessary to evaluate the consequence of the temperature on the electromechanical performance of the machine, namely the torque-speed operating area and power factor.For power factor, it is important to evaluate it to estimate the efficiency and properly design the power electronics components [10], [11].It has been established in multiple studies, that the low power factor of a SynRM machine is a natural limitation due to the saliency [12]- [14].It has also been demonstrated that having a high-power factor and a high efficiency at the same time may be conflicting objectives.As an example, in [12], the choice of design has to be made by balancing the compromise between power factor and efficiency (Figure 3).A higher power factor design may lead to a lower efficiency, therefore a higher badness indicator.119 The operating area is also important to be reevaluated to make sure that the targeted operating points required by the application are still attainable despite the temperature variation.[15]- [17] for example, have shown the importance of the thermal effects to be properly included in a system performance study.This is valid in different perspectives including for a performance prediction or state-observer and optimum control.Furthermore, in a magnetless SynRM machine, the consequence may be less obvious compared to a permanentmagnet motor, has been studied in different literature such as [18]- [20].Despite being relatively common knowledge as shown in several references cited, this study's contribution will be specifically in identifying the operating area and power factor variation for the SynRM with the segmented rotor, in an automotive equipment application.
In the following section, a methodology section will explain how the resistance variation due to temperature will be computed, then integrated into a validated analytical model that will output the power factor and torque-speed operating area.Then, the results section will present the variation of torque-speed range and power factor depending on the winding resistance variation.A tool presented in the form of abacus shows the relevance of the study where examples of non-attainable operating points due to resistance increase (temperature increase) will be presented.

METHODOLOGY
To evaluate the influence of temperature on the torque-speed operating area and power factor, a validated analytical tools was developed, validated and then used.In this section we will start with detailing how the temperature variation is taken into account as a variation of resistance.Then the details on the development of the analytical model, followed by the validation experiments are presented.

Winding resistance variation in relation to temperature variation
In our magnetless SynRM, the component that is sensitive and can change behavior with the temperature is winding.Its resistance is temperature dependent.The DC resistance of the copper wire increases with increasing temperature by (1) [21]: Where for a copper conductor,   is the resistance of copper at temperature ,  0 is the resistance of copper at 20 °C ( 20 ), and  is the temperature correction coefficient of copper which is equal to 0.00393/°C.As the temperature increases, the winding resistance will also increase proportionally.Therefore, throughout this article, the influence of the temperature is reflected by the variation of the winding resistance.The initial value of the winding resistance at 20 °C is reported to be at 0.22 Ω [4].Figure 4(a) shows the rise of winding resistance as the temperature increases.It is known that as a consequence, the copper losses in the machine also increase with temperature.Figure 4(b) shows the variation of the copper losses at the different operating current levels as the temperature varies in the range of 20−200 °C.On the other hand, the variation of power factor and operating area are not as self-evident, which this study tries to answer.This paper will be divided into two sections: The first explains the implementation of an analytical model to compute the power factor and operating area complete with its validation.After that, a section will present the observation and analysis of the results.

Development of the analytical model for torque-speed operating area and power factor
Deduced from an equivalent circuit, a phasor diagram with properly evaluated parameters can be a versatile tool to evaluate the electromechanical performance of an electrical machine without using any costly numerical tools.The SynRM machine phasor diagram allows us to evaluate different parameters depending on the available input [22].A tool for fast evaluation of the electromechanical performance using the phasor diagram was developed and presented in [23].The tools take as input the inductances and the resistance value, then compute the torque-speed operating area using an algorithm that can be described as in Figure 5.
To use the phasor diagram, the inductances were deduced previously using the reluctance network model, and validated by FEA [4], [24].The machine was designed so that minimum saturation only occurred at the maximum current, therefore the inductances were considered constant.The voltage and current will be swept across a range up to 14 V/50 A which corresponds to an automotive battery's maximum voltage and current.The resistance is the variable that we are going to manipulate as input.The output that we are going to evaluate is first, the torque-speed operating area, and then the power factor ().
For a given power supply (, ), and a load angle control (), set of equations from the phasor diagram helps in deducing the speed envelope, power factor, and efficiency.In (2) relates the current with the torque produced while in (3) relates the voltages with the speed [25].Finally, the power factor can be deduced from the phasor diagram by evaluating the angle between the voltage and current in (4).The computation of the torque-speed operating area and the power factor are then validated experimentally.

Experimental validation of the analytical model
The prototype machine was mounted on a test bench as shown in Figure 6.The bench is controlled by a Dspace Micro-Autobox with a command built in Simulink.It is integrated with a Rapid-Pro power unit module for power electronics, integrated with voltage measurement and shunt for current measurement.All The motor is equipped with an incremental encoder with 500 points of resolution.A hysteresis brake serves as load and a torque sensor is used to capture the dynamic torque.

Figure 6. The SynRM test bench
Several operating points of the machine were tested by operating the machine to a constant speed and applying a load (Γexp).This is done by controlling the machine using speed control and applying load braking.The resulting current and voltage from operating the machine experimentally at (Γexp, Nexp) were then injected into the computation tool to validate the computed torque and speed (Γcomp, Ncomp).Figure 7 shows the experimental and computed torque Figure 7 The next performance criteria computation to be validated is the power factor cosϕ.At a given load angle (here β = 45°, which is the maximum-torque load angle), by maintaining the motor at a constant speed using a speed control at no load, the current and voltage on a winding phase were recorded.The experimental phase shift at different steady-state speeds was later calculated and compared to the computed power factor (Figure 8).Comparison between experimental and computed power factors for speeds ranging from 500 rpm to 5000 rpm shows that the computation tool gives a correct trend and is robust with maximum error on the  1).Having validated the analytical tools for the computation of torquespeed operating area and power factor, the influence of resistance variation (image of temperature variation) on the torque-speed operating area and the power factor can be assessed.This will be presented in the results and analysis section.

RESULTS AND ANALYSIS
We have seen in the introduction that the increase in temperature is reflected in the increase in the winding resistance.All the results presented in the results section are a function of resistance variation, which is an image of a potential temperature variation presented in Figure 4 Here.There are 2 significant findings presented: The reduction of the torque-speed operating area (section 3.1) and the increase of power factor due to increasing temperature.Following these findings, a tool of maximum speed and power factor tracking as a function of winding resistance (which depends on temperature) is developed and presented in section 3.

Reduction of torque-speed operating area due to temperature
Using in ( 1) and ( 2) that was implemented in the computation tool, the torque-speed operating area can be plotted following variation of the value of resistance.Figure 9  It is shown that as the resistance increases, at a fixed current (torque) level, the maximum speed attainable is reduced.At higher torque, the reduction is more important compared to the one at a low torque point, and the reduction percentage is increasing quadratically due to the sum of the square of the speed in (2) previously shown.This means that due to copper losses, the power output is limited, and this is reflected in the reduction of the maximum speed attainable.The reduction of the maximum speed means that certain operating points at maximum power on the edge of the operating area envelope may not be attainable at higher temperatures.For example, at 60 °C, our winding resistance will be increased up to more than 0.25 Ω, and this will prevent us from attaining the operating point of (0.5 N.m, 5000 rpm).Figure 9. Variation of the operating area as a function of winding resistance Rs for a power supply limited to (50 A,14 V)

Power factor increase due to temperature
The power factor is known to be directly related to the speed and load angle of the machine by looking at its phasor diagram.Figure 10 shows the power factor of the SynRM machine plotted against the load angle for different speeds ranging from 1000 to 6000 rpm, which is the operating speed of our application.From the graph, we can see that the increase in speed would decrease the power factor across the machine operating points.On the other hand, the increase in load angle tends to increase the power factor up to a certain maximum point.For our SynRM prototype machine, that angle is at  = 75°.
Additional to the influence of load angle and speed on the power factor, there is also the variation of power factor due to the increase in temperature.Figure 11 shows the variation of power factor as the winding resistance increases at different operating speeds.Unlike the operating area, the increase in winding resistance has increased the power factor.This is explained by the higher resistance terms compared to the inductance terms in (3), which reduce the reactive power by consequence.This behavior confirms the findings in the literature such as in [10]- [12] the power factor handicap of operating at higher speed is therefore compensated when the winding resistance is higher.As an example, the power factor of the machine with a resistance of 0.05 Ω operating at 6000 rpm can be increased from 0.55 up to 0.84 if the resistance is increased to 0.25 Ω.The increase of 0.29 in power factor is certainly consequent in terms of power electronics components and may lead to a potential increase in efficiency.For comparison, with a resistance of 0.05 Ω, same power factor (0.84) can only be achieved if the machine operates at a maximum speed of 1100 rpm (between blue and cyan lines).It is nonetheless an arguable choice to sacrifice in terms of losses by adding the copper losses, which need to be evaluated properly in future studies.

Tools: abacus for tracking maximum speed and power factor
In previous sections, it has been shown that the maximum speed attainable and the power factor are affected by the increase of temperature through the increase of the winding resistance.To help designers to track the potential degradation of speed and increase of power factor as a function of winding resistance, an abacus combining the results previously presented was built.Figure 12 shows the abacus.
Figure 12.The abacus gives the speed limit at different current levels and power factor at different speeds as a function of winding resistance On the right axis, the maximum speed for different currents (torque) can be found, plotted in dotted lines.The maximum speed was computed for a maximum voltage supply of 14 V.As the winding resistance increases, we can track the degradation of maximum speed for different current levels.On the left side, the reading of the axis gives the power factor at different speed levels, plotted in full lines.
With this graphical tool, a simple measurement of the winding resistance in real time can let us know the power factor and the maximum speed available for the machine.For example, for an operating point (, ) of (0.57 N.m, 3500 rpm) where the current is at 50 A (from the reading of Figure 9), the winding resistance should not exceed 0.2 Ω, or else, the speed will not be achievable.The maximum speed at this torque is indicated by the orange dotted lines.At the same time, if the winding resistance is at 0.2 Ω, the power factor can be expected to be at around 0.9.This is an area between the yellow and brown full lines.

CONCLUSIONS AND PERSPECTIVES
In this study, an analytical model using the phasor diagram of the SynRM machine was built to identify the operating area and power factor.The computation using the tool has been validated on the prototype test bench.Using the validated model, the influence of temperature on the operating area and power factor was evaluated.We found that the maximum speed attainable by the machine is quadratically reduced with temperature increase.The power factor on the other hand is increased with the temperature.An abacus for maximum speed and power factor tracking was built following the findings to guide the user of the machine.Having the abacus for maximum speed and power factor tracking, a potential coupling between the thermal model previously developed with the abacus could further relate the motor utilization cycle to not only the winding temperature but also the power factor and operating area variation.

Figure 1 .Figure 2 .
Figure 1.Design and dimensions of the SynRM prototype machine

Figure 3 .
Figure3.The scatter plot relating the power factor and efficiency following a design optimization to find the best design of a SynRM machine by[12]

Figure 4 .
Figure 4. Influence of temperature on (a) SynRM winding resistance and (b) copper losses at different operating currents

Figure 5 .
Figure 5.The flow chart of the algorithm used for the construction of the torque-speed area and deduction of power factor using the phasor diagram [23] Int J Pow Elec & Dri Syst ISSN: 2088-8694  Influence of temperature on power factor and operating area … (Mohd Azri Hizami Rasid) 121 the parameters managed by Micro-Autobox are observable from a host PC and are recorded for post-treatment.

Figure 7 .
Figure 7. Operating point validation at equal current and voltage for both computation and experiments for: (a) torque and (b) speed

Figure 8 .
Figure 8. Experimental current-voltage phase shift observed and the corresponding computed operating diagram at: (a)  = 500 rpm and (b)  = 2000 rpm.ϕ is the angle between the current (blue vector) and the voltage (black vector) shows the torque-speed operating area N = 500 rpm N = 2000 rpm Int J Pow Elec & Dri Syst ISSN: 2088-8694  Influence of temperature on power factor and operating area … (Mohd Azri Hizami Rasid) 123 of the machine plotted for different values of winding resistance ranging from 0.05 to 0.25 Ω which are potential values of our winding resistance.

Table 1 .
Computed and experimental cos ϕ comparison