Measuring Quadrature and Direct Current

Introduction

This application note provides guidance for making measurements relating to field-oriented control of electric motors and presents an example use case that illustrates how to accomplish these with the /MT1 option on a Yokogawa Test&Measurement DL950 ScopeCorder. Specifically addressed are direct and quadrature currents of a surface-mounted permanent magnet motor with field weakening applied. The techniques discussed are also applicable to other field-oriented control variables, algorithms, and motor technologies.
 

Background

Field-oriented control (FOC) is employed by motor controllers (inverters) to streamline the management of multi-phase motors and is achieved by applying a DC control model at the input, which simplifies the complex AC commutation output. This approach enables the inverter’s proportional-integral (PI) control loop to effectively regulate select non-time-varying DC variables and treats the AC motor as if it were a DC motor. With a wound DC motor, which consists of stator winding responsible for flux magnetization and armature winding for torque generation, FOC manipulates the modeled winding currents to control torque and speed.

The rotor of a permanent magnet motor has its own magnetic field that is generated by magnets mounted on the surface or interior of the rotor. By applying AC current to the stator windings, a rotating magnetic field is produced which prompts the rotor to track the stator. For FOC, the stator current is often represented in polar coordinates, where the vertical axis signifies quadrature current and the horizontal axis represents direct current. The electrical angle or load angle (θ) denotes the angle between the stator current and the quadrature or direct axis, which symbolizes the displacement of the rotor and stator magnetic fields.

In the case of a surface-mounted permanent magnet (SMPM) motor, the segment of current directed in the positive quadrature direction (Iq) generates torque equivalent to DC armature current, while a negative current in the direct axis (Id) diminishes torque and resembles a DC magnetizing current. To optimize torque in this motor type, orient the stator current 90 degrees from the direct axis to ensure no direct axis current (Id = 0) and full stator current in the quadrature direction.

Figure 1. Full torque, Id=0.
 

Users may opt to operate a motor at a heightened speed, though this risks sacrificing torque generation. In such instances, the inverter encounters limitations imposed by the back electromotive force (BEMF) produced by the rotor’s magnetic flux. This limitation occurs as the BEMF approaches the DC supply bus voltage or encounters constraints posed by component limits (e.g., capacitor voltages or conductor sizes). To mitigate the impact of BEMF, a strategy known as field weakening is employed, where the stator flux is aligned in opposition to the rotor’s magnetic flux to reduce overall flux in the airgap. If SMPM motors are in use, this reduction is accomplished by applying a negative direct current to alter the load angle of the stator current concerning the rotor position (referenced to the direct or quadrature axis).

Figure 2.  Negative Id under field weakening of a SMPM.

Figure 3. Visual representation of direct and quadrature axis with two-pole motor.
 

Id, Iq in Motor Control

Motor controllers perform instantaneous measurements of voltages, currents, and rotor position and enable real-time computation of direct and quadrature currents. PI controllers utilize DC values for comparison with user- or algorithm-defined setpoints. Error terms are then calculated and corrections applied to voltage signals accordingly.

The application of Clarke and Park transforms is instrumental when determining equations for the computation of direct and quadrature currents from the instantaneous values of phase currents and rotor position. Clarke transform facilitates the representation of a three-phase system through two-phase orthogonal variables (α and β) in a stationary reference frame. Park transform incorporates these variables along with the rotor position (electrical angle Θ) to compute the direct and quadrature currents referenced to the rotating reference frame. The Figure 4 motor control diagram shows these measurements, associated waveforms, and example equations for Clarke and Park transforms.

Figure 4. Example simplified equations commonly used in the microcontroller libraries provided by semiconductor manufacturers.
 

Sensing Requirements

To calculate the direct and quadrature currents, an instrument must measure both phase currents and the rotor’s mechanical position. Phase currents are usually measured with a current probe, current transformer, or direct instrument input and the mechanical rotor position determined by equipping the motor with either a rotary encoder or resolver. Often these devices are embedded in the motor itself or added to the motor or load motor side of a dynamometer. The instrumentation must be capable of assessing both the instantaneous values and phase of the current as well as computing positional information and displacements from raw sensor signals.
 

Understanding Encoder/Resolver Alignment

To understand the relative angular position of the stator current (Is) and to compute Id and Iq components, it is necessary to measure the position of the rotor shaft. The accuracy of this position depends upon how the sensor itself is fitted to the rotor shaft relative to the magnets inside the rotor (direct axis). Ideally, the sensor position is directly referenced to either the direct or quadrature axis. However, fitting a sensor in a test situation by hand may not be possible and there must be compensation for this in Id and Iq computations.

One compensation method for sensor alignment is comparing its positional information with the BEMF voltage of the motor when it is spun unloaded (i.e., disconnected inverter and unloaded shaft). With no load, Id and Iq = 0 and the zero-crossing of the BEMF voltage waveform can be used as a reference. The peak phase voltage of the BEMF signal occurs when aligned with the direct axis of the rotor, whereas the zero-crossing of the BEMF occurs when aligned with the quadrature axis (90 degrees).

Figure 5. Sensor orientation with respect to rotor position.
 

Be careful to recognize that if line-to-line voltage is used for BEMF measurement, an additional 30-degree shift must be added due to the angular spacing between phase current and phase voltage in a delta connection (see vector diagrams for delta wired voltmeters). This 30-degree offset should be programmed into the instrument as a correction value in addition to any additional displacement (such as zerocrossing to z pulse).

Figure 6. Direct and quadrature axis relative to BEMF voltage.
 

Another way to calibrate the offset is to fit an encoder or resolver on the dyno dedicated for instrumentation purposes only. In this configuration the angular offset is set between the z pulse and the q axis while the motor is under load and being driven by the inverter using its own positional feedback device (e.g., encoder, resolver, hall, pll). With the inverter, motor, instrumentation, and encoder or resolver connected and running, the inverter demands a positive quadrature current and a zero direct current (Iq > 0, Id = 0). This locates the sensor’s reference to the quadrature axis as known by the inverter, which means the direct axis is 90 degrees away from the quadrature axis.

This can also compensate for motor controllers (which perform an alignment on each startup) and effectively moves the inverter’s reference point, and this can be an offset count of A and B pulses rather than the z pulse. Figure 7 shows an example of this using the z pulse of an encoder.

Figure 7. Example of encoder z pulse offset from q and d axis under load phase A when inverter command is Id=0.
 

ScopeCorder Computations

The DL950 ScopeCorder, a hybrid instrument that bridges the divide between an oscilloscope and data acquisition tools, provides both streaming and triggered waveforms and boasts a diverse range of input types and advanced computations tailored specifically for mechatronic systems. A unique feature is its capacity for real-time mathematical computations via its /MT1 function. Using this feature, signals are multiplied directly at the A/D converter for simultaneous acquisition of both raw and computed data.

Notably, these calculations are performed on incoming signals rather than on captured waveforms, as observed in traditional scopes. This distinction enables implementation of triggers on real-time mathematical channels. When computing direct and quadrature components, the DL950 ScopeCorder excels in calculating FOC parameters in real time and computes crucial metrics such as electrical angles, motor power signals, and quadrature and direct vectors. The calculation structure for determining Id and Iq derives from the Clarke Park Theorem.

Figure 8. This display shows the instantaneous current waveforms, electrical angle, Clarke transform, and Park transform resulting in Id and Iq. Also trended is the CAN controlled signal of Id and Iq from the VCU.
 

Figure 9. This image shows a larger time scale with response of Id and Iq with respect to the CAN values dictated by the VCU.
 

Id and Iq Analysis Setup

The /MT1 option on the DL950 ScopeCorder streamlines configuration and analysis of FOC measurements. Users can easily select voltage and current channels, configure position sensor translation, and input constant parameters specific to the motor under test.

Step 1
Select the Motor Analysis (/MT1) option in the Application window.

Figure 10. View of /MT1 option.

Step 2
Select the appropriate number of motor systems for analysis.

Figure 11. Motor system selection options.

Step 3
Select inputs and configure motor channels by choosing the proper wiring scheme, corresponding voltage, and current signals. DC power can also be set up if applicable.

Figure 12. Initial view of Source options.

Step 4
Use the Angle setup to configure the position sensor. A pop-out window will open to display position sensor types from which to choose (e.g., ABZ Encoder or Resolver). For each configuration, select the channels needed for analysis and the multiplication factor needed to represent electrical angle. Exit the pop-out window to display the updated sensor configuration.

Figure 13. Configuring the position sensor.

Step 5
Use the Analysis menu to designate the calculation period based on the synchronous signal that establishes timing basis for power calculations. This source can also be filtered out to effectively remove high-frequency content that might modulate the zero-crossing. Additional options in this view allow users to define power calculation analysis types, rms type, angle scale, reactive power formula, and use the integration setup to determine time basis for power consumption measurements.

Figure 14. Designating the calculation period.

Step 6
Input the constants to the motor and position sensor, the number of poles, flux linkage (Webers), and winding resistance (Ohms), and then determine if the rotational speed to be output as RPMs or frequency (Hertz). Next, select whether to perform fundamental analysis or power invariant analysis. Fundamental analysis uses only fundamental frequency (power driving frequency) to make motor and power calculations, whereas power invariant analysis compensates for a line-to-line voltage measurement by scaling the signal by a factor of sqrt(2/3).

Figure 15. View of Motor tab where constants, number of poles, and more are input.

Step 7
Input the θe offset, which refers to the electrical angle offset between incoming signals of the motor and the falling edge of the position signal.

Figure 16. Determining the θe offset in the Motor tab view.

Step 8
The coordinate plane now depicts the voltage and current vectors and displays the values for voltage, current, and inductance in both quadrature and direct planes to ensure appropriate configuration.

Figure 17. Example of a coordinate plane generated from user inputs.

Step 9
Configure efficiency measurements to show losses that can be found on component and system levels, then set up the torque signal for mechanical power calculation, either as a scaled analog signal or a decoded frequency signal that provides torque value.

Figure 18. View of Efficiency tab.

Step 10
In the Realtime Waveform menu, select the DQ and delta-star calculations to be output as real-time math channels (with a much higher sampling rate of up to 10MS/s). This action utilizes real-time math resources and enables higher resolution for analysis.

Figure 19. View of Realtime Waveform tab.

Step 11
To complete the setup for FOC and motor analysis, select and trend motor and power measurements in the Display menu. This provides a digital multimeter reading of incoming signals and helps users determine which signals should be turned on and trended for further analysis.

Figure 20. Example Id and Iq measurement results from using the /MT1 option.
 

Conclusion

The /MT1 option on the DL950 ScopeCorder from Yokogawa Test&Measurement streamlines setup and analysis of FOC measurements and motor parameters. Easy to use, /MT1 allows users to focus on actual measurements versus wasting precious time with tedious setup procedures to more efficiently extract valuable insights from their motor systems.